GIFT   OF 

ASSOCIATED  ELECTRICAL   AND 
MECHANICAL   ENGINEERS 


MECHANICS  DEPARTMENT 


Engineering 
Library 


UNiV    CALIF 


ROOM 


ELEMENTARY 


ELECTRICITY   AND   MAGNETISM 


11'alker  &•  liontall  sc 

MAGNETIC   CHART   OF   THE   BRITISH   ISLANDS, 

SHOWING     THE     LINES     OF     EQUAL     MAGNETIC     DECLINATION     AND 
THOSE    OF    EQUAL    MAGNETIC    DIP. 

iv 


ELEMENTAL!  LESSONS 


IN 


ELECTRICITY  &  MAGNETISM 


BY 

SILVANUS   P.    THOMPSON, 
v 

D.Sc.,  B.A.,  F.E.S.,  F.R.A.S. 

PRINCIPAL  OF  AND   PROFESSOR   OF  PHYSICS   IN  THE   CITY   AND  GUILDS  OF 

LONDON   TECHNICAL   COLLEGE,    FINSBURY  ; 

LATE   PROFESSOR   OF   EXPERIMENTAL   PHYSICS    IN 

UNIVERSITY    COLLEGE,    BRISTOL 


NEW   EDITION,  REVISED  THROUGHOUT 
WITH  ADDITIONS 


MACMILLAN    AiNTD    CO. 

AND      LONDON 
1895 

All  rig  Jits  reserved 


/ 


Engineering 
Library 


MPT. 


COPYRIGHT,  1894, 
BY  MACMILLAN  AND  CO. 


Set  up  and  electrotyped  December,  1894.       Reprinted 
June,  1895. 


Norfoooti 

J.  S.  Gushing  &  Co.  -  Berwick  &  Smith. 
Norwood,  Mass.,  U.S.A. 


PKEFACE 

THESE  Elementary  Lessons  have  now  been  largely  re- 
written. The  considerable"  changes  made  have  been 
necessitated  not  only  by  the  progress  of  the  science  but 
by  the  piracy,  covert  as  well  as  open,  to  which  since  its 
appearance  in  1881  the  book  has  been  subjected. 

In  the  thirteen  years  which  have  elapsed  much  addi- 
tion has  been  made  to  our  knowledge,  and  many  points 
then  in  controversy  have  been  settled.  The  system  of 
electric  units,  elaborated  first  by  the  British  Association 
and  subsequently  in  several  International  Congresses,  is 
now  legalized  in  the  chief  civilized  countries.  New  mag- 
netic surveys  —  in  England  by  Thorpe  and  Riicker,  in 
the  United  States  under  Mendenhall  —  have  enabled  new 
magnetic  charts  to  be  prepared  for  the  epoch  1900  A.D. 
The  researches  of  Ewing,  Hopkinson,  and  others  on  the 
magnetic  properties  of  iron,  and  the  general  recognition 
of  the  principle  of  the  magnetic  circuit,  have  advanced 
the  science  of  magnetism,  to  which  also  Swing's  molecu- 
lar theory  has  given  an  added  interest.  The  properties 
of  alternate  currents,  of  which  in  1881  little  was  known, 
have  been  forced  into  study  by  the  extension  of  their 
industrial  uses  in  telephony  and  in  electric  lighting. 
vii 


749219 


vm  ELECTRICITY  AND   MAGNETISM 

Entirely  new  is  the  use  of  polyphase  alternate  currents 
and  rotatory  magnetic  fields  for  the  electric  transmission 
of  power.  Transformers  have  come  into  extensive  em- 
ployment for  the  distribution  at  low-pressure  of  electric 
energy  which  has  been  transmitted  from  a  generating 
station  at  high-pressure.  Accumulators  for  the  storage 
of  electric  energy  have  become  of  great  commercial  im- 
portance. Electric  lamps,  large  and  small,  illuminate  in 
millions  our  cities,  towns,  villages  and  ships.  Electric 
currents  for  lighting  and  power  are  now  supplied  publicly 
on  a  very  large  scale  from  central  stations  operated  by 
steam  or  water  power.  Supply-meters  are  in  regular  use, 
and  measuring  instruments  of  many  forms  have  come 
into  the  market. 

Along  with  these  advances  in  practice  there  has  been 
a  110  less  striking  progress  in  theory.  The  ideas  of  Fara- 
day, as  enlarged  and  developed  by  Clerk  Maxwell,  were 
in  1881  only  beginning  to  be  understood  and  appreciated 
outside  a  narrow  circle.  In  1894,  thanks  largely  to  the 
labours  of  Heaviside,  Hertz,  Lodge,  Poyntiiig,  Fitzgerald, 
Boltzmann,  Poincare,  and  others,  they  are  everywhere 
accepted.  In  1881  Maxwell's  electromagnetic  theory  of 
light  —  a  conception  not  less  far-reaching  than  the  theory 
of  the  conservation  of  energy  —  was  deemed  of  doubtful 
probability  :  it  was  not  yet  accepted  by  such  great  masters 
as  Lord  Kelvin  or  Von  Helinholtz.  Though  adopted  by 
the  younger  generation  of  British  physicists,  it  needed  the 
experimental  researches  of  Hertz  and  of  Lodge  upon  the 
propagation  of  electric  waves  to  demonstrate  its  truth  to 
their  brethren  in  Germany,  France,  and  America.  Even 
now,  after  the  most  convincing  experimental  verifications 


PREFACE 


of  Maxwell's  splendid  generalization  that  light-waves  are 
really  electric  waves,  many  of  the  logical  consequences  of 
Maxwell's  teaching  are  still  ignored  or  misunderstood. 
It  is  still,  to  many,  a  hard  saying  that  in  an  electric 
circuit  the  conducting  wire  though  it  guides  does  not 
carry  the  energy  :  that  the  energy-paths  lie  outside  in 
the  surrounding  medium,  not  inside  within  the  so-called 
conductor.  That  the  guttapercha  sheath,  and  not  the 
copper  wire  within  it,  is  the  actual  medium  which  con- 
veys the  impulse  from  one  side  of  the  Atlantic  to  the 
other  in  cable-telegraphy,  is  still  incredible  to  those 
brought  up  in  the  older  school  of  thought.  But  it  is 
none  the  less  a  necessary  consequence  of  the  views  which 
the  inescapable  logic  of  facts  drove  Maxwell  and  his 
followers  to  adopt. 

This  expansion  of  the  science  and  of  its  practical 
applications  has  rendered  more  difficult  than  before  the 
task  of  presenting  with  sufficient  clearness,  yet  with 
necessary  brevity,  an  elementary  exposition  of  the  lead- 
ing phenomena,  and  of  their  relations  to  one  another. 

The  author  is  under  obligations  to  many  scientific 
friends  for  data  of  which  he  has  made  use.  He  is  under 
special  obligations  to  his  assistant,  Mr.  Miles  Walker,  for 
indefatigable  proof-reading  and  revision  of  the  Problems 
and  Index. 

LONDON,  September  1894. 


CONTENTS 

part  Jfftat 

CHAPTER    I 
FRICTIONAL  ELECTRICITY 

LESSON  PAGE 

I.  Electric  Attraction  and  Repulsion      ...  1 

II.  Electroscopes 15 

III.  Electrification  by  Influence          ....  24 

IV.  Conduction  and  Distribution  of  Electricity         .  35 
V.  Electric  Machines 47 

VI.  The  Leyden  Jar  and  other  Condensers        .        .  68 

VII.  Other  Sources  of  Electrification  .  77 


CHAPTER    II 

MAGNETISM 

VIII.  Magnetic  Attraction  and  Repulsion    ...  89 

IX.  Methods  of  making  Magnets       ....  99 

X.  Distribution  of  Magnetism 106 

XI.  Laws  of  Magnetic  Force 117 

Note  on  Ways  of  Reckoning  Angles  and  Solid  Angles  133 

XII.  Terrestrial  Magnetism 136 

xi 


xii  ELECTRICITY  AND   MAGNETISM 


CHAPTER    III 

CURRENT  ELECTRICITY 
LESSON  PAGE 

XIII.  Simple  Voltaic  Cells 147 

XIV.  Chemical  Actions  in  the  Cell        .         .         .157 
XV.  Voltaic  Cells 163 

XVI.  Magnetic  Actions  of  the  Current  .         .        .181 

XVII.  Galvanometers 193 

XVIII.  Currents  produced  by  Induction  .         .         .210 
XIX.  Chemical  Actions  of  the  Currents         .         .     223 
XX.  Physical    and  Physiological   Effects  of    the 

Current  234 


Skcottti 

CHAPTER    IV 

ELECTROSTATICS 

XXI.  Theory  of  Potential 244 

Note  on  Fundamental  and  Derived  Units        .  263 

XXII.  Electrometers 267 

XXIII.  Dielectric  Capacity,  etc 277 

XXIV.  Phenomena  of  Discharge       ....  293 
XXV.  Atmospheric  Electricity        ....  316 

CHAPTER    V 
ELECTROMAGNETICS 

XXVI.  Magnetic  Potential        .        .         .    '    .        .327 

XXVII.  The  Electromagnetic  System  of  Units  .         .  344 
XXVIII.  Properties  of  Iron  and  Steel .         .         .         .354 

XXIX.  Diamagnetism 363 

XXX.  The  Magnetic  Circuit 369 

XXXI.  Electromagnets 374 

XXXII.  Electrodynamics   .                          ...  384 


CONTENTS  xiii 


CHAPTER    VI 
MEASUREMENT  OF  CURRENTS,  ETC. 

LESSON  PAGE 

XXXIII.  Ohm's  Law  and  its  Consequences       .         .     397 

XXXIV.  Electrical  Measurements    .  ,    412 


CHAPTER    VII 
THERMO-ELECTRICITY 
XXXV.  Thermo-Electric  Currents  .        .        .        .426 

CHAPTER    VIII 
HEAT,  POWER,  AND  LIGHT,  FROM  ELECTRIC  CURRENTS 

XXXVI.  Heating  Effects  of  Currents        .        .         .435 
XXXVII.  Electric  Energy  :  its  Supply  and  Measure- 
ment         441 

XXXVIII.  Electric  Motors  (Electromagnetic  Engines)     448 
XXXIX.  Electric  Light     ...,,.     455 

CHAPTER    IX 
INDUCTANCE 

XL.  Mutual  Induction 464 

XLI.  Self-induction 468 

CHAPTER    X 

DYNAMOS  AND  TRANSFORMERS 

XLII.  Magneto-electric  and  Dynamo-electric  Gen- 
erators   476 

XLIII.   Alternate  Currents 486 

XLIV.  Alternate-current  Generators     .         .         .  495 

XLV.  Transformers 500 

XL VI.  Alternate-current  Motors   .  ,  504 


xiv  ELECTRICITY  AND   MAGNETISM 


CHAPTER    XI 

ELECTRO-CHEMISTRY 

LESSON  PAGE 

XL VII.  Electrolysis 508 

XLVIII.  Accumulators 518 

XLIX.  Electrodeposition 520 


CHAPTER    XII 
TELEGRAPHY 

L.  Electric  Telegraphs 525 

LI.  Cable  Telegraphy 541 

LII.  Miscellaneous  Telegraphs       ....     543 

CHAPTER    XIII 

TELEPHONY 
LIU.  Telephones    .        .        .        .      .  .        .        •     547 

CHAPTER    XIV 
ELECTRIC  WAVES 

LIV.  Oscillations  and  Waves 554 

LV.  The  Electromagnetic  Theory  of  Light   .        .  558 
LVI.  Other  Relations  between  Light  and    Elec- 
tricity           566 


CONTENTS  xv 


APPENDIX 

PAGE 

APPENDIX  A.  TABLE  OF  ANGLES  AND  SOLID  ANGLES  574 
APPENDIX  B.  ABSTRACT  OF  BULLETIN  OF  U.  S.  COAST 

AND  GEODETIC  SURVEY  ......  576 

APPENDIX  C.  OFFICIAL  SPECIFICATION  FOR  THE 

PREPARATION  OF  THE  CLARK  STANDARD  CELL  .  579 

PROBLEMS  AND  EXERCISES  ......  582 

INDEX 609 

MAGNETIC  CHART  OF  THE  BRITISH  ISLANDS  Frontispiece 
MAGNETIC  MAP  OF  THE  UNITED  STATES  '* 


ELEMENTAKY   LESSONS 

ON 

ELECTRICITY   &  MAGNETISM 


$art  Jftrst 


CHAPTER  I 

FRICTIONAL    ELECTRICITY 

LESSON  I.  —  Electric  Attraction  and  Repulsion 

1.  Electricity.  —  Electricity  is  the  name  given  to  an 
invisible  agent  known  to  us  only  by  the  effects  which  it 
produces  and  by  various  manifestations  called  electrical. 
These  manifestations,  at  first  obscure  and  even  mysterious, 
are  now  well  understood ;  though  little  is  yet  known  of 
the  precise  nature  of  electricity  itself.  It  is  neither 
matter  nor  energy ;  yet  it  apparently  can  be  associated 
or  combined  with  matter;  and  energy  can  be  spent  in 
moving  it.  Indeed  its  great  importance  to  mankind 
arises  from  the  circumstance  that  by  its  means  energy 
spent  in  generating  electric  forces  in  one  part  of  a  system 
can  be  made  to  reappear  as  electric  heat  or  light  or  work 
at  some  other  part  of  the  system ;  such  transfer  of  energy 
taking  place  even  to  very  great  distances  at  an  enor- 
mous speed.  Electricity  is  apparently  as  indestructible  as 
B  1 


ELECTRICITY  AND   MAGNETISM       TART  i 


matter  or  as  energy.  It  can  neither  be  created  nor 
destroyed,  but  it  can  be  transformed  in  its  relations  to 
matter  and  to  energy,  and  it  can  be  moved  from  one  place 
to  another.  In  many  ways  its  behaviour  resembles  that 
of  an  incompressible  liquid;  in  other  ways  that  of  a 
highly  attenuated  and  weightless  gas.  It  appears  to  exist 
distributed  nearly  uniformly  throughout  all  space.  Many 
persons  (including  the  author)  are  disposed  to  consider  it 
as  identical  with  the  luminiferous  ether.  If  it  be  not  the 
same  thing,  there  is  an  intimate  relation  between  the  two. 
That  this  must  be  so,  is  a  necessary  result  of  the  great 
discovery  of  Maxwell — the  greatest  scientific  discovery  of 
the  nineteenth  century — that  light  itself  is  an  electric 
phenomenon,  and  that  the  light-waves  are  merely  electric, 
or,  as  he  put  it,  electromagnetic  waves. 

The  name  electricity  is  also  given  to  that  branch  of 
science  which  deals  with  electric  phenomena  and  theories. 
The  phenomena,  and  the  science  which  deals  with  them, 
fall  under  four  heads.  The  manifestations  of  electricity 
when  standing  still  are  different  from  those  of  electricity 
moving  or  flowing  along :  hence  we  have  to  consider 
separately  the  properties  of  (i.)  statical  charges,  and  those 
of  (ii.)  currents.  Further,  electricity  whirling  round  or  in 
circulation  possesses  properties  which  were  independently 
discovered  under  the  name  of  (iii.)  magnetism.  Lastly, 
electricity  when  in  a  state  of  rapid  vibration  manifests 
new  properties  not  possessed  in  any  of  the  previous  states, 
and  causes  the  propagation  of  (iv.)  waves.  These  four 
branches  of  the  science  of  electricity  are,  however,  closely 
connected.  The  object  of  the  present  work  is  to  give  the 
reader  a  general  view  of  the  main  facts  and  their  simple 
relations  to  one  another. 

If?  these  first  lessons  we  begin  with  charges  of 
electricity,  their  production  by  friction,  by  influence,  and 
by  various  other  means,  and  shall  study  them  mainly  by 
the  manifestations  of  attraction  and  repulsion  to  which 
they  give  rise.  After  that  we  go  on  to  magnetism  and 


CHAP.    I 


ELECTRIC  ATTRACTION 


currents,  and  the  relations  between  them.  The  subject  of 
electric  waves  is  briefly  discussed  at  the  end  of  the  book. 
2.  Electric  Attraction.  —  If  you  take  a  piece  of  seal- 
ing-wax, or  of  resin,  or  a  glass  rod,  and  rub  it  upon  a 
piece  of  flannel  or  silk,  it  will  be  found  to  have  acquired 
a  property  which  it  did  not  previously  possess :  namely, 
the  power  of  attracting  to  itself  such  light  bodies  as  chaff, 
or  dust,  or  bits  of  paper  (Fig.  1).  This  curious  power 


Fig.  1. 

was  originally  discovered  to  be  a  property  of  amber,  or, 
as  the  Greeks  called  it,  ^AeKT/ooi/,  which  is  mentioned  by 
Thales  of  Miletus  (B.C.  600),  and  by  Theophrastus  in  his 
treatise  on  Gems,  as  attracting  light  bodies  when  rubbed. 
Although  an  enormous  number  of  substances  possess  this 
property,  amber  and  jet  were  the  only  two  in  which  its 
existence  had  been  recognized  by  the  ancients,  or  even 
down  to  so  late  a  date  as  the  time  of  Queen  Elizabeth. 


ELECTRICITY   AND   MAGNETISM        PART  i 


Fig.  2. 


About  the  year  1600,  Dr.  Gilbert  of  Colchester  discovered 

by  experiment  that  not 
only  amber  and  jet,  but  a 
very  large  number  of  sub- 
stances, such  as  diamond, 
sapphire,  rock-crystal,  glass, 
sulphur,  sealing-wax,  resin, 
etc.,  which  he  styled  elec- 
trics,* possess  the  same  pro- 
perty. Ever  since  his  time 
the  name  electricity  f  has 
been  employed  to  denote  the 
agency  at  work  in  producing 
these  phenomena.  Gilbert 
also  remarked  that  these  ex- 
periments are  spoiled  by  the 
presence  of  moisture. 
3.  Further  Experiments.  —  A  better  way  of  observ- 
ing the  attracting  force  is  to  employ  a  small  ball  of  elder 
pith,  or  of  cork,  hung 
by  a  fine  thread  from  a 
support,  as  shown  in 
Fig.  2.  A  dry  warm 
glass  tube,  excited  by 
rubbing  it  briskly  with 
a  silk  handkerchief, 
will  attract  the  pith- 
ball  strongly,  showing 
that  it  is  highly  electri- 
fied. The  most  suit-  :  ,  — 
able  rubber,  if  a  stick  "^ 
of  sealing-wax  is  used, 
will  be  found  to  be 
flannel,  woollen  cloth,  or,  best  of  all,  fur.  Boyle  discovered 


Fig.  3. 


*  "  Electrica;  qnae  attrahunt  eadem  ratione  ut  electrum  "  (Gilbert). 
t  The  first  work  in  which  this  term  was  used  is  that  of  Robert  Boyle, 
On  the  Mechanical  Production  of  Electricity,  published  at  Oxford  in  1675. 


CHAP,  i      ELECTRIFICATION   BY    FRICTION  5 

that  an  electrified  body  is  itself  attracted  by  one  that 
has  not  been  electrified.  This  may  be  verified  (see 
Fig.  3)  by  rubbing  a  stick  of  sealing-wax,  or  a  glass 
rod,  arid  hanging  it  in  a  wire  loop  at  the  end  of  a  silk 
thread.  If,  then,  the  hand  be  held  out  towards  the 
suspended  electrified  body,  the  latter  will  turn  round 
and  approach  the  hand.  So,  again,  a  piece  of  silk  ribbon, 
if  rubbed  with  warm  indiarubber,  or  even  if  drawn 
between  two  pieces  of  warm  flannel,  and  then  hung  up 
by  one  end,  will  be  found  to  be  attracted  by  objects 
presented  to  it.  If  held  near  the  wall  of  the  room  it  will 
fly  to  it  and  stick  to  it.  With  proper  precautions  it  can 
be  shown  that  both  the  rubber  and  the  thing  rubbed  are 
in  an  electrified  state,  for  both  will  attract  light  bodies ; 
but  to  show  this,  care  must  be  taken  not  to  handle  the 
rubber  too  much.  Thus,  if  it  is  desired  to  show  that 
when  a  piece  of  fur  is  rubbed  upon  sealing-wax,  the  fur 
becomes  also  electrified,  it  is  better  not  to  take  the  fur  in 
the  hand,  but  to  cement  it  to  the  end  of  a  glass  rod  as  a 
handle.  The  reason  of  this  precaution  will  be  explained 
toward  the  close  of  this  lesson,  and  more  fully  in  Lesson 
IV. 

A  large  number  of  substances,  including  iron,  gold, 
brass,  and  all  the  metals,  when  held  in  the  hand  and 
rubbed,  exhibit  no  sign  of  electrification,  —  that  is  to  say, 
do  not  attract  light  bodies  as  rubbed  amber  and  rubbed 
glass  do.  Gilbert  mentions  also  pearls,  marble,  agate, 
arid  the  lodestone,  as  substances  not  excited  electrically 
by  rubbing  them.  Such  bodies  were,  on  that  account, 
formerly  termed  non-electrics ;  but  the  term  is  erroneous, 
for  if  they  are  mounted  on  glass  handles  and  then  rubbed 
with  silk  or  fur,  they  behave  as  electrics. 

4.  Electric  Repulsion. — When  experimenting,  as  in 
Fig.  1,  with  a  rubbed  glass  rod  and  bits  of  chopped  paper, 
or  straw,  or  bran,  it  will  be  noticed  that  these  little 
bits  are  first  attracted  and  fly  up  towards  the  excited  rod, 
but  that,  having  touched  it,  they  are  speedily  repelled 


ELECTRICITY   AND   MAGNETISM       PART  i 


and  fly  back  to  the  table.     To  show  this  repulsion  better, 

let  a  small  piece  of  feather  or  down  be  hung  by  a  silk 

thread  to  a  support,  and 
let  an  electrified  glass  rod 
be  held  near  it.  It  will 
dart  towards  the  rod  and 
stick  to  it,  and  a  moment 
later  will  dart  away  from 
it,  repelled  by  an  invisible 
force  (Fig.  4),  nor  will  it 
again  dart  towards  the 
rod.  If  the  experiment 
be  repeated  with  another 
feather  and  a  stick  of 
sealing-wax  rubbed  on 
flannel  the  same  effects 
will  occur.  But,  if  now 
the  hand  be  held  towards 
the  feather,  it  will  rush 

toward  the  hand,  as  the  rubbed  body  (in  Fig.  3)  did. 

This  proves  that  the  feather,  though  it  has  not  itself  been 

rubbed,  possesses  the 

property      originally 

imparted  to  the  rod 

l>y   rubbing   it.      In 

fact,   it  has   become 

electrified,  by  having 

touched  an  electrified 

body  which  has  given 

part  of  its  electricity 

to  it.     It  would  ap- 

pear then   that   two 


bodies  electrified  will  i 

the  same  electrifica- 

tion    repel    one    an- 

other.    This  may  be  confirmed  by  a  further  experiment. 

A  rubbed  glass  rod,  hung  up  as  in  Fig  3,  is  repelled  by  a 


CHAP,  i        OPPOSITE   ELECTRIC   STATES  7 

similar  rubbed  glass  rod  ;  while  a  rubbed  stick  of  sealing- 
wax  is  repelled  by  a  second  rubbed  stick  of  sealing-wax. 
Another  way  of  showing  the  repulsion  between  two 
similarly  electrified  bodies  is  to  hang  a  couple  of  small 
pith-balls,  by  thin  linen  threads  to  a  glass  support,  as 
in  Fig.  5,  and  then  touch  them  both  with  a  rubbed  glass 
rod.  They  repel  one  another  and  fly  apart,  instead  of 
hanging  down  side  by  side,  while  the  near  presence  of 
the  glass  rod  will  make  them  open  out  still  wider,  for 
now  it  repels  them  both.  The  self-repulsion  of  the  parts 
of  an  electrified  body  is  beautifully  illustrated  by  the 
experiment  of  electrifying  a  soap-bubble,  which  expands 
when  electrified. 

5.  Two  Kinds  of  Electrification.  —  Electrified  bodies 
do  not,  however,  always  repel  one  another.  The  feather 
which  (see  Fig.  4)  has  been  touched  by  a  rubbed  glass 
rod,  and  which  in  consequence  is  repelled  from  the 
rubbed  glass,  will  be  attracted  if  a  stick  of  rubbed  seal- 
ing-wax be  presented  to  it ;  and  conversely,  if  the  feather 
has  been  first  electrified  by  touching  it  with  the  rubbed 
sealing-wax,  it  will  be  attracted  to  a  rubbed  glass  rod, 
though  repelled  by  the  rubbed  wax.  So,  again,  a  rubbed 
glass  rod  suspended  as  in  Fig.  3  will  be  attracted  by  a 
rubbed  piece  of  sealing-wax,  or  resin,  or  amber,  though 
repelled  by  a  rubbed  piece  of  glass.  The  two  pith-balls 
touched  (as  in  Fig.  5)  with  a  rubbed  glass  rod  fly  from 
one  another  by  repulsion,  and,  as  we  have  seen,  fly  wider 
asunder  when  the  excited  glass  rod  is  held  near  them ; 
yet  they  fall  nearer  together  when  a  rubbed  piece  of 
sealing-wax  is  held  under  them,  being  attracted  by  it. 
Symmer  first  observed  such  phenomena  as  these,  and 
they  were  independently  discovered  by  Du  Fay,  who 
suggested  in  explanation  of  them  that  there  were  two 
different  kinds  of  electricity  which  attracted  one  another 
while  each  repelled  itself.  The  electricity  produced  on 
glass  by  rubbing  it  with  silk  he  called  vitreous  electricity, 
supposing,  though  erroneously,  that  glass  could  yield  no 


8  ELECTRICITY   AND   MAGNETISM       PART  i 

other  kind  ;  and  the  electricity  excited  in  such  substances 
as  sealing-wax,  resin,  shellac,  iodiarubber,  and  amber, 
by  rubbing  them  on  wool  or  flannel,  he  termed  resinous 
electricity.  The  kind  of  electricity  produced  is,  however, 
found  to  depend  not  only  on  the  thing  rubbed  but  on  the 
rubber  also ;  for  glass  yields  "  resinous  "  electricity  when 
rubbed  with  a  cat's  skin,  and  resin  yields  "vitreous1' 
electricity  if  rubbed  with  a  soft  amalgam  of  tin  and 
mercury  spread  on  leather.  Hence  these  names  have 
been  abandoned  in  favour  of  the  more  appropriate  terms 
introduced  by  Franklin,  who  called  the  electricity  excited 
upon  glass  by  rubbing  it  with  silk  positive  electricity,  and 
that  produced  on  resinous  bodies  by  friction  with  wool  or 
fur,  negative  electricity.  The  observations  of  Sy miner 
and  Du  Fay  may  therefore  be  stated  as  follows :  —  Two 
positively  electrified  bodies  apparently  repel  one  another : 
two  negatively  electrified  bodies  apparently  repel  one 
another :  but  a  positively  electrified  body  and  a  negatively 
electrified  body  apparently  attract  one  another.  It  is 
now  known  that  these  effects  which  appear  like  a  repul- 
sion and  an  attraction  between  bodies  at  a  distance  from 
one  another  are  really  due  to  actions  going  on  in  the 
medium  between  them.  The  positive  charge  does  not 
really  attract  the  negative  charge  that  is  near  it ;  but 
both  are  urged  toward  one  another  by  stresses  in  the 
medium  in  the  intervening  space. 

6.  Simultaneous  Production  of  both  Electrical  States. 
—  Neither  kind  of  electrification  is  produced  alone ; 
there  is  always  an  equal  quantity  of  both  kinds  pro- 
duced ;  one  kind  appearing  on  the  thing  rubbed  and  an 
equal  amount  of  the  other  kind  on  the  rubber.  The 
clearest  proof  that  these  amounts  are  equal  can  be  given 
in  some  cases.  For  it  is  found  that  if  both  the  —  electricity 
of  the  rubber  and  the  +  electricity  of  the  thing  rubbed  be 
imparted  to  a  third  body,  that  third  body  will  show  no 
electrification  at  all,  the  two  equal  and  opposite  electrifica- 
tions having  exactly  neutralized  each  other.  A  simple 


CHAP,  i          THEORIES   OF  ELECTRICITY  9 

experiment  consists  in  rubbing  together  a  disk  of  sealing- 
wax  and  one  covered  with  flannel,  both  being  held  by 
insulating  handles.  To  test  them  is  required  an  insulated 
pot  and  an  electroscope,  as  in  Fig.  29.  If  either  disk  be 
inserted  in  the  pot  the  leaves  of  the  electroscope  will 
diverge ;  but  if  both  are  inserted  at  the  same  time  the 
leaves  do  not  diverge,  showing  that  the  two  charges  on 
the  disks  are  equal  and  of  opposite  sign. 

In  the  following  list  the  bodies  are  arranged  in  such  an 
order  that  if  any  two  be  rubbed  together  the  one  which 
stands  earlier  in  the  series  becomes  positively  electrified, 
and  the  one  that  stands  later  negatively  electrified :  — 
Fur,  wool,  ivory,  glass,  silk,  metals,  sulphur,  indiarubber, 
guttapercha,  collodion,  or  celluloid. 

7.  Theories  of  Electricity.  —  Several  theories  have 
been  advanced  to  account  for  these  phenomena,  but  all 
are  more  or  less  unsatisfactory.  Symmer  proposed  a 
"two-fluid"  theory,  according  to  which  there  are  two 
imponderable  electric  fluids  of  opposite  kinds,  which 
neutralize  one  another  when  they  combine,  and  which 
exist  combined  in  equal  quantities  in  all  bodies  until 
their  condition  is  disturbed  by  friction.  A  modification 
of  this  theory  was  made  by  Franklin,  who  proposed 
instead  a  "  one-fluid "  theory,  according  to  which  there 
is  a  single  electric  fluid  distributed  usually  uniformly 
in  all  bodies,  but  which,  when  they  are  subjected  to 
friction,  distributes  itself  unequally  between  the  rubber 
and  the  thing  rubbed,  one  having  more  of  the  fluid,  the 
other  less,  than  the  average.  Hence  the  terms  positive 
and  negative,  which  are  still  retained ;  that  body  which  is 
supposed  to  have  an  excess  being  said  to  be  charged  with 
positive  electricity  (usually  denoted  by  the  plus  sign  +), 
while  that  which  is  supposed  to  have  less  is  said  to  be 
charged  with  negative  electricity  (and  is  denoted  by 
the  minus  sign  — ).  These  terms  are,  however,  purely 
arbitrary,  for  in  the  present  state  of  science  we  do  not 
know  which  of  these  two  states  really  means  more  and 


10  ELECTRICITY   AND   MAGNETISM       PART  i 

which  means  less.  In  many  ways  electricity  behaves  as 
a  weightless  substance  as  incompressible  as  any  material 
liquid.  It  is,  however,  quite  certain  that  electricity  is  not 
a  material  fluid,  whatever  else  it  may  be.  For  while  it 
resembles  a  fluid  in  its  property  of  apparently  flowing 
from  one  point  to  another,  it  differs  from  every  known 
fluid  in  almost  every  other  respect.  It  possesses  no 
weight;  it  repels  itself.  It  is,  moreover,  quite  impossible 
to  conceive  of  two  fluids  whose  properties  should  in  every 
respect  be  the  precise  opposites  of  one  another.  For 
these  reasons  it  is  clearly  misleading  to  speak  of  an 
electric  fluid  or  fluids,  however  convenient  the  term  may 
seem  to  be.  In  metals  and  other  good  conductors  elec- 
tricity can  apparently  move  and  flow  quite  easily  in 
currents.  In  transparent  solids,  such  as  glass  and  resin, 
and  in  many  transparent  liquids  such  as  oils,  and  in 
gases  such  as  the  air  (if  still,  and  not  rarefied)  electricity 
apparently  cannot  flow.  Even  a  vacuum  appears  to  be  a 
non-conductor.  In  the  case  of  all  non-conductors  elec- 
tricity can  only  be  moved  by  an  action  known  as  displace- 
ment (see  Art.  57). 

It  appears  then  that  in  metals  electricity  can  easily 
pass  from  molecule  to  molecule ;  but  in  the  case  of  non- 
conductors the  electricity  is  in  some  way  stuck  to  the 
molecules,  or  associated  with  them.  Some  electricians, 
notably  Faraday,  have  propounded  a  molecular  theory 
of  electricity,  according  to  which  the  electrical  states  are 
the  result  of  certain  peculiar  conditions  of  the  molecules 
of  the  surfaces  that  have  been  rubbed.  Another  view  is 
to  regard  the  state  of  electrification  as  related  to  the  ether 
(the  highly-attenuated  medium  which  fills  all  space,  and 
is  the  vehicle  by  which  light  is  transmitted),  which  is 
known  to  be  associated  with  the  molecules  of  matter. 
Some  indeed  hold  that  the  ether  itself  is  electricity;  and 
that  the  two  states  of  positive  and  negative  electrifica- 
tion are  simply  due  to  displacement  of  the  ether  at  the 
surfaces  of  bodies.  In  these  lessons  we  shall  avoid  as 


CHAP,  i  ELECTRIC   CHARGES  11 

far  as  possible  all  theories,  and  shall  be  content  to  use 
the  term  electricity. 

8.  Charge.  —  The  quantity  of  electrification  of  either 
kind  produced  by  friction  or  other  means  upon  the  surface 
of  a  body  is  spoken  of  as  a  charge,  and  a  body  when 
electrified  is  said  to  be  charged.     It  is  clear  that  there 
may  be  charges  of  different  values  as  well  as  of  either 
kind.     When  the  charge  of  electricity  is  removed  from 
a  charged  body  it  is  said  to  be  discharged.     Good  con- 
ductors of  electricity  are  instantaneously  discharged  if 
touched  by  the  hand  or  by  any  conductor  in  contact  with 
the  ground,  the  charge  thus  finding  a  means  of  escaping 
to  earth  or  to  surrounding  walls.     A  body  that  is  not  a 
good  conductor  may  be  readily  discharged  by  passing  it 
rapidly  through  the  flame  of  a  spirit-lamp  or  a  candle; 
for  the  hot  gases  instantly  carry  off  the  charge  and  dis- 
sipate it  in  the  air. 

Electricity  may  either  reside  upon  the  surface  of  bodies 
as  a  charge,  or  flow  through  their  substance  as  a  current. 
That  branch  of  the  science  which  treats  of  the  laws  of  the 
charges,  that  is  to  say,  of  electricity  at  rest,  upon  the 
surface  of  bodies  is  termed  electrostatics,  and  is  dealt 
with  in  Chapter  IV.  The  branch  of  the  subject  which 
treats  of  the  flow  of  electricity  in  currents  is  dealt  with 
in  Chapter  III.,  and  other  later  portions  of  this  book. 

9.  Modes    of    representing    Electrification.  —  Several 
modes  are  used  to  represent  the  electrification  of  surfaces. 
In  Figs.  6,  7,  and  8  are  rep- 
resented two  disks  —  A  cov- 
ered with  woollen  cloth,  B 

of  some  resinous  body,  — 
which  have  been  rubbed  to- 
gether so  that  A  has  become 
positively,  B  negatively  elec- 

Trifled.     In   Fi|.  6  the  sur-     «*  6'          Fl"  T'          "*  8' 
faces  are  marked  with  plus  (  +  )  and  minus  (  — )  signs. 
In  Fig.  7  dotted  lines  are  drawn  just  outside  the  posi- 


12  ELECTRICITY   AND   MAGNETISM       PART  i 

lively  electrified  surface  and  just  within  the  negatively 
electrified  surface,  as  though  one  had  a  surplus  and  the 
other  a  deficit  of  electricity.  In  Fig.  8  lines  are  drawn 
across  the  intervening  space  from  the  positively  electrified 
surface  to  the  opposite  negative  charge.  The  advantages 
of  this  last  mode  are  explained  in  Art.  13. 

10.  Conductors    and    Insulators.  —  The    term    "con- 
ductors," used  above,  is  applied  to  those  bodies  which 
readily  allow  electricity  to  flow  through  them.     Roughly 
speaking,  bodies  may  be  divided  into  two  classes  —  those 
which  conduct  and  those  which    do  not;    though   very 
many  substances  are  partial  conductors,  and  cannot  well 
be  classed  in  either  category.     All  the  metals   conduct 
well ;  the  human  body  conducts,  and  so  does  water.     On 
the  other  hand  glass,    sealing-wax,  silk,  shellac,  gutta- 
percha,   indiarubber,   resin,   fatty   substances   generally, 
and  the  air,  are  non-conductors.     On  this  account  these 
substances  are  used  to  make  supports  and  handles  for 
electrical  apparatus  where  it  is  important  that  the  elec- 
tricity should  not  leak  away ;  hence  they  are  sometimes 
called  insulators  or  isolators.     Faraday  termed  them  dielec- 
trics.    We  have  remarked  above  that  the  name  of  non- 
electrics  was  given  to   those  substances  which,  like  the 
metals,  yield  no  sign  of  electrification  when  held  in  the 
hand  and  rubbed.     We  now  know  the  reason  why  they 
show  no  electrification ;  for,  being  good  conductors,  the 
electrification  flows  away  as  fast  as  it  is  generated.     The 
observation   of   Gilbert  that  electrical   experiments   fail 
in  damp  weather  is  also  explained  by  the  knowledge  that 
water  is  a  conductor,  the  film  of  moisture  on  the  surface 
of  damp  bodies  causing  the  electricity  produced  by  friction 
to  leak  away  as  fast  as  it  is  generated. 

11.  Other  Electrical  Effects.  —  The  production  of  elec- 
tricity by  friction  is  attested  by  other  effects  than  those 
of    attraction    and    repulsion,    which    hitherto   we   have 
assumed  to   be  the  test  of  the  presence  of  electricity. 
Otto  von  Guericke  first  observed  that  sparks  and  flashes 


CHAP,  i       SOURCES   OF   ELECTRIFICATION  13 

of  light  could  be  obtained  from  highly  electrified  bodies 
at  the  moment  when  they  were  discharged.  Such  sparks 
are  usually  accompanied  by  a  snapping  sound,  suggesting 
on  a  small  scale  the  thunder  accompanying  the  lightning 
spark,  as  was  remarked  by  Newton  and  other  early 
observers.  Pale  flashes  of  light  are  also  produced  by  the 
discharge  of  electricity  through  tubes  partially  exhausted 
of  air  by  the  air-pump.  Other  effects  will  be  noticed  in 
due  coarse. 

12.  Other  Sources  of  Electrification.  —  The  student 
must  be  reminded  that  friction  is  by  no  means  the  only 
source  of  electrification.  The  other  sources,  percussion, 
compression,  heat,  chemical  action,  physiological  action, 
contact  of  metals,  etc.,  will  be  treated  of  in  Lesson  VII. 
We  will  simply  remark  here  that  friction  between  two 
different  substances  always  produces  electrical  separa- 
tion, no  matter  what  the  substances  may  be.  Syrnmer 
observed  the  production  of  electrification  when  a  silk 
stocking  was  drawn  over  a  woollen  one,  though  woollen 
rubbed  upon  woollen,  or  silk  rubbed  upon  silk,  produces 
no  electrical  effect.  If,  however,  a  piece  of  rough  glass 
be  rubbed  on  a  piece  of  smooth  glass,  electrification  is 
observed ;  and  indeed  the  conditions  of  the  surface  play 
a  very  important  part  in  the  production  of  electrification 
by  friction.  In  general,  of  two  bodies  thus  rubbed 
together,  that  one  becomes  negatively  electrical  whose 
particles  are  the  more  easily  removed  by  friction.  Differ- 
ences of  temperature  also  affect  the  electrical  conditions 
of  bodies,  a  warm  body  being  usually  negative  when 
rubbed  on  a  cold  piece  of  the  same  substance.  The 
quantity  of  electrification  produced  is,  however,  not  pro- 
portional to  the  amount  of  the  actual  mechanical  friction  ; 
hence  it  appears  doubtful  whether  friction  is  truly  the 
cause  of  the  electrification.  Something  certainly  happens 
when  the  surfaces  of  two  different  substances  are  brought 
into  intimate  contact,  which  has  the  result  that  when 
they  are  drawn  apart  they  are  found  (provided  at  least 


14  ELECTRICITY   AND   MAGNETISM        PART  i 

one  of  them  is  a  non-conductor)  to  have  acquired  opposite 
charges  of  electrification ;  one  surface  having  apparently 
taken  some  electricity  from  the  other.  But  these  opposite 
charges  attract  one  another  and  cannot  be  drawn  apart 
without  there  being  mechanical  work  done  upon  the 
system.  The  work  thus  spent  is  stored  up  in  the  act 
of  separating  the  charged  surfaces;  and  as  long  as 
the  charges  remain  separated  they  constitute  a  store 
of  potential  energy.  The  so-called  frictional  electric 
machines  are  therefore  machines  for  bringing  dissimilar 
substances  into  intimate  contact,  and  then  drawing  apart 
the  particles  that  have  touched  one  another  and  become 
electrical. 

If  the  two  bodies  that  are  rubbed  together  are  both 
good  conductors,  they  will  riot  become  strongly  electrified, 
even  if  held  on  insulating  handles.  It  is  quite  likely, 
however,  that  the  heat  produced  by  friction,  as  in  the 
bearings  of  machinery,  is  due  to  electric  currents  gen- 
erated where  the  surfaces  meet  and  slip. 

13.  Electric  Field.  —  Whenever  two  oppositely 
charged  surfaces  are  placed  near  one  another  they  tend 
to  move  together,  and  the  space  between  them  is  found 
to  be  thrown  into  a  peculiar  state  of 
stress,  as  though  the  medium  in  between 
had  been  stretched.  To  explore  the 
space  between  two  bodies  one  of  which 
has  been  positively  and  the  other  nega- 
tively electrified,  we  may  use  a  light 
pointer  (Fig.  0)  made  of  a  small  piece  of  very  thin  paper 
pierced  with  a  hole  through  which  passes  a  long  thread 
of  glass.  It  will  be  found  that  this  pointer  tends  to 
point  across  from  the  positively  electrified  surface  to 
the  negatively  electrified  surface,  along  invisible  lines  of 
electric  force.  The  space  so  filled  with  electric  lines  of 
force  is  called  an  electric  field.  In  Fig.  8  A  and  B 
represent  two  bodies  the  surfaces  of  which  have  been 
electrified,  the  one  positively,  the  other  negatively.  In 


CHAP,  i  ELECTROSCOPES  15 

the   field  between   them   the   electric   lines  pass  across 

almost  straight,  except  near  the  edges,  where  they  are 

curved.     Electric  lines  of  force  start  from  a  positively 

charged  surface  at  one  end,  and 

end    on    a    negatively  charged 

surface  at  the  other  end.     They 

never  meet  or  cross  one  another. 

Their  direction  indicates  that  of 

the   resultant  electric   force   at 

every  point  through  which  they 

pass.    The  stress  in  the  medium 

thus  mapped  out  by  the  lines  of 

force   acts   as   a  tension    along 

them,  as  though  they  tended  to 

shorten  themselves.     In  fact  in  Fig.  8  the  tension  in  the 

medium  draws  the  two  surfaces  together.     There  is  also 

a  pressure  in  the  medium  at  right  angles  to  the  lines, 

tending  to  widen  the  distance  between  them.     Fig.  10 

represents  a  ball  which  has  been  positively  electrified, 

and  placed  at  a  distance  from  other  objects;  the  lines  in 

the  field  being  simply  radial. 

LESSON  II.  —  Electroscopes 

14.  Simple  Electroscopes. —  An  instrument  for  detect- 
ing whether  a  body  is  electrified  or  not,  and  whether 
the  electrification  is  positive  or  negative,  is  termed  an 
Electroscope.      The  feather  which  was  attracted  or  re- 
pelled, and  the  two  pith-balls  which  flew  apart,  as  we 
found  in  Lesson  I.,  are  in  reality  simple  electroscopes. 
There  are,  however,  a  number  of   pieces   of   apparatus 
better  adapted  for  this  particular  purpose,  some  of  which 
we  will  describe. 

15.  Needle  Electroscope.  —  The  earliest  electroscope 
was  that  devised  by  Dr.  Gilbert,  and  shown  in  Fig.  11, 
which  consists  of  a  stiff  strip  balanced  lightly  upon  a 
sharp  point.     A  thin  strip  of  brass  or  wood,  a  straw,  or 


16 


ELECTRICITY   AND   MAGNETISM        PART 


even  a  goose  quill,  balanced  upon  a  sewing  needle,  will 
serve  equally  well.     When  an  electrified  body  is  held  near 


I 


Fig.  11, 

the  electroscope  it  is  attracted  and  turned  round,  and  will 
thus  indicate  the  presence  of  electric  charges  1'ar  too  feeble 
to  attract  bits  of  paper  from  a  table. 

16.    Gold-Leaf    Electroscope.  —  A    still    more    sen  si- 


Fig.  12. 

tive  instrument  is  the  Gold-Leaf  Electroscope,  invented 
by  Bennet,  and  shown  in  Fig.  12.  We  have  seen 
how  two  pith-balls  when  similarly  electrified  repel  one 


CHAP,  i          GOLD-LEAF   ELECTROSCOPE  17 

another  and  stand  apart,  gravity  being  partly  overcome 
by  the  force  of  the  electric  repulsion.  A  couple  of 
narrow  strips  of  the  thinnest  tissue  paper,  hung  upon  a 
support,  will  behave  similarly  when  electrified.  But  the 
best  results  are  obtained  with  two  strips  of  gold  leaf, 
which,  being  excessively  thin,  is  much  lighter  than  the 
thinnest  paper.  The  Gold -Leaf  Electroscope  is  con- 
veniently made  by  suspending  the  two  leaves  within  a 
wide-mouthed  glass  jar,  which  both  serves  to  protect 
them  from  draughts  of  air  and  to  support  them  from 
contact  with  the  ground.  The  mouth  of  the  jar  should 
be  closed  by  a  plug  of  paraffin  wax,  through  which  is 
pushed  a  bit  of  varnished  glass  tube.  Through  this 
passes  a  stiff  brass  wire,  the  lower  end  of  which  is  bent 
at  a  right  angle  to  receive  the  two  strips  of  gold  leaf, 
while  the  upper  supports  a  flat  plate  of  metal,  or  may  be 
furnished  with  a  brass  knob.  When  kept  dry  and  free 
from  dust  it  will  indicate  excessively  small  quantities  of 
electrification.  A  rubbed  glass  rod,  even  while  two  or 
three  feet  from  the  instrument,  will  cause  the  leaves  to 
repel  one  another.  The  chips  produced  by  sharpening  a 
pencil,  falling  on  the  electroscope  top,  are  seen  to  be 
electrified.  If  the  knob  be  even  brushed  with  a  small 
camel's  hair  brush,  the  slight  friction  produces  a  percep- 
tible effect.  With  this  instrument  all  kinds  of  friction 
can  be  shown  to  produce  electrification.  Let  a  person, 
standing  upon  an  insulating  support,  —  such  as  a  stool 
with  glass  legs,  or  a  board  supported  on  four  glass 
tumblers,  —  be  briskly  struck  with  a  silk  handkerchief, 
or  with  a  fox's  tail,  or  even  brushed  with  a  clothes  brush, 
he  will  be  electrified,  as  will  be  indicated  by  the  electro- 
scope if  he  place  one  hand  on  the  knob  at  the  top  of  it. 
The  Gold-Leaf  Electroscope  can  further  be  used  to  indi- 
cate the  kind  of  electrification  on  an  excited  body.  ThuB, 
suppose  we  rubbed  a  piece  of  brown  paper  with  a  piece  of 
indiarubber  and  desired  to  find  out  whether  the  electri- 
fication excited  on  the  paper  was  +  or  — ,  we  should 
c 


18 


ELECTRICITY   AND   MAGNETISM        PART  i 


proceed  as  follows  :  —  First  charge  the  gold  leaves  of  the 
electroscope  by  touching  the  knob  with  a  glass  rod  rubbed 
on  silk.  The  leaves  diverge,  being  electrified  with  -f 
electrification.  When  they  are  thus  charged  the  approach 
of  a  body  which  is  positively  electrified  will  cause  them 
to  diverge  still  more  widely  ;  while,  on  the  approach  of 
one  negatively  electrified,  they  will  tend  to  close  together. 
If  now  the  brown  paper  be  brought  near  the  electroscope, 
the  leaves  will  be  seen  to  diverge  more,  proving  the 
electrification  of  the  paper  to  be  of  the  same  kind  as 
that  with  which  the  electroscope  is  charged,  or  positive. 

Sometimes  the  outer  surface 
of  the  glass  jar  containing 
the  gold  leaves  is  covered 
with  wire  gauze  or  strips  of 
foil  to  shield  the  leaves  from 
the  influence  of  external 
bodies.  A  preferable  way  is 
to  use  glass  of  a  kind  that 
conducts. 

The  part  played  by  the 
surrounding  medium  in  the 
operation  of  the  electroscope 
is  illustrated  by  Fig.  13. 
Of  the  electric  lines  in  the 


Fig.  13. 


field  surrounding  the  rubbed  rod  a  number  will  pass  into 
the  metal  cap  of  the  electroscope  and  emerge  below 
through  the  leaves.  The  nearer  the  rod  is  brought,  the 
greater  will  be  the  number  of  electric  lines  thus  affecting 
the  instrument.  There  being  a  tension  along  the  lines 
and  a  pressure  across  them,  the  effect  is  to  draw  the  gold 
leaves  apart  as  though  they  repelled  each  other. 

The  Gold-Leaf  Electroscope  will  also  indicate  roughly 
the  amount  of  electrification  on  a  body  placed  in  contact 
with  it,  for  the  gold  leaves  open  out  more  widely  when 
the  charge  thus  imparted  to  them  is  greater.  For  exact 
measurement,  however,  of  the  degree  of  electrification, 


ELECTROSCOPE 


recourse   must   be   had    to    the   instruments    known   as 
Electrometers,  described  in  Lesson  XXTI. 

In  another  form  of  electroscope  (Bohnenberger's)  a 
single  gold  leaf  is  used,  and  is  suspended  between  two 
metallic  plates,  one  of  which  can  be  positively,  the  other 
negatively  electrified,  by  placing  them  in  communication 
with  the  poles  of  a  "dry  pile"  (Art.  193).  If  the  gold 
leaf  be  charged  positively  or  negatively  it  will  be  attracted 
to  one  side  and  repelled  from  the  other,  according  to  the 
law  of  attraction  and  repulsion  mentioned  in  Art.  4. 

17.  Henley's  Semaphore.  —  As  an  indicator  for  large 
charges  of  electricity  there  is  sometimes  used  a  sema- 
phore like  that  shown  in  Fig.  14. 
It  consists  of  a  pith-ball  at  the  end 
of  a  light  arm  fixed  on  a  pivot  to 
an  upright.  When  the  whole  is 
electrified  the  pith-ball  is  repelled 
from  the  upright  and  flies  out  at  an 
angle,  indicated  on  a  graduated 
scale  or  dial  behind  it.  This  little 
electroscope,  which  is  seldom  used 
except  to  show  whether  an  electric 
machine  or  a  Leyden  battery  is 
charged,  must  on  no  account  be  con- 
fused with  the  delicate  "  Quadrant 
Electrometer"  described  in  Lesson 


Fig.  14. 


XXII.,  whose  object  is  to  measure  very  small  charges  of 
electricity  —  not  to  indicate  large  ones. 

18.  The  Torsion  Balance.  —  Although  more  properly 
an  Electrometer  than  a  mere  Electroscope,  it  will  be 
most  convenient  to  describe  here  the  instrument  known 
as  the  Torsion  Balance  (Fig.  15).  This  instrument,  once 
famous,  but  now  quite  obsolete,  served  to  measure  the 
force  of  the  repulsion  between  two  similarly  electrified 
bodies,  by  balancing  the  repelling  force  against  the  force 
exerted  by  a  fine  wire  in  untwisting  itself  after  it  has 
been  twisted.  The  torsion  balance  consists  of  a  light  arm 


20  ELECTRICITY   AND   MAGNETISM       PART  i 

or  lever  of  shellac  suspended  within  a  cylindrical  glass 
case  by  means  of  a  fine  silver  wire.  At  one  end  this 
lever  is  furnished  with  a  gilt  pith-ball  n.  The  upper 
end  of  the  silver  wire  is  fastened  to  a  brass  top,  upon 

which  a  circle,  divided 
into  degrees,  is  cut.  This 
top  can  be  turned  round 
in  the  tube  which  sup- 
ports it,  and  is  called  the 
torsion-head.  Through  an 
aperture  in  the  cover  there 
can  be  introduced  a  sec- 
ond gilt  pith-ball  m,  fixed 
to  the  end  of  a  vertical 
glass  rod  a.  Round  the 
glass  case,  at  the  level  of 
the  pith-balls,  a  circle  is 
drawn,  and  divided  also 
into  degrees. 

In  using  the  torsion 

balance  to  measure  the  amount  of  a  charge  of  electricity, 
the  following  method  is  adopted  :  —  First,  the  torsion-head 
is  turned  round  until  the  two  pith-balls  m  and  n  just 
touch  one  another.  Then  the  glass  rod  a  is  taken  out, 
and  the  charge  of  electricity  to  be  measured  is  imparted 
to  the  ball  m,  which  is  then  replaced  in  the  balance.  As 
soon  as  m  and  n  touch  one  another,  part  of  the  charge 
passes  from  m  to  n,  and  they  repel  one  another  because 
they  are  then  similarly  electrified.  The  ball  n,  therefore, 
is  driven  round  and  twists  the  wire  up  to  a  certain  extent. 
The  force  of  repulsion  becomes  less  and  less  as  n  gets 
farther  and  farther  from  m;  but  the  force  of  the  twist 
gets  greater  and  greater  the  more  the  wire  is  twisted. 
Hence  these  two  forces  will  balance  one  another  when 
the  balls  are  separated  by  a  certain  distance,  and  it  is 
clear  that  a  large  charge  of  electricity  will  repel  the  ball 
n  with  a  greater  force  than  a  lesser  charge  would.  The 


CHAP,  i          LAW   OF   INVERSE   SQUARES  21 

distance  through  which  the  ball  is  repelled  is  read  off  in 
angular  degrees  of  the  scale.  When  a  wire  is  twisted, 
the  force  with  which  it  tends  to  untwist  is  precisely  pro- 
portional to  the  amount  of  the  twist.  The  force  required 
to  twist  the  wire  ten  degrees  is  just  ten  times  as  great 
as  the  force  required  to  twist  it  one  degree.  In  other 
words,  the  force  of  torsion  is  proportional  to  the  angle  of 
torsion.  The  angular  distance  between  the  two  balls  is, 
when  they  are  not  very  widely  separated,  very  nearly 
proportional  to  the  actual  straight  distance  between  them, 
and  represents  the  force  exerted  between  electrified  balls 
at  that  distance  apart.  The  student  must,  however,  care- 
fully distinguish  between  the  measurement  of  the  force 
and  the  measurement  of  the  actual  quantity  of  electricity 
with  which  the  instrument  is  charged.  For  the  force 
exerted  between  the  electrified  balls  will  vary  at  different 
distances  according  to  a  particular  law  known  as  the 
"law  of  inverse  squares,"  which  requires  to  be  carefully 
explained. 

19.  The  Law  of  Inverse  Squares.  —  Coulomb  proved, 
by  means  of  the  Torsion  Balance,  that  the  force  exerted 
between  two  small  electrified  bodies  varies  inversely  as 
the  square  of  the  distance  between  them  when  the 
distance  is  varied.  Thus,  suppose  two  small  electrified 
bodies  1  inch  apart  repel  one  another  with  a  certain 
force,  at  a  distance  of  2  inches  the  force  will  be  found 
to  be  only  one  quarter  as  great  as  the  force  at  1  inch  ; 
and  at  10  inches  it  will  be  only  T^7  part  as  great  as 
at  1  inch.  This  law  is  proved  by  the  following  ex- 
periment with  the  torsion  balance.  The  two  scales  were 
adjusted  to  0°,  and  a  certain  charge  was  then  imparted 
to  the  balls.  The  ball  n  was  repelled  round  to  a  distance 
of  36°.  The  twist  on  the  wire  between  its  upper  and 
lower  ends  was  also  36°,  or  the  force  tending  to  repel 
was  thirty-six  times  as  great  as  the  force  required  to 
twist  the  wire  by  1°.  The  torsion-head  was  now  turned 
round  so  as  to  twist  the  thread  at  the  top  and  force 


ELECTRICITY  AND   MAGNETISM       PART  i 

the  ball  n  nearer  to  m,  and  was  turned  round  until 
the  distance  between  n  and  m  was  halved.  To  bring 
down  this  distance  from  36°  to  18°,  it  was  found 
needful  to  twist  the  torsion-head  through  126°.  The 
total  twist  between  the  upper  and  lower  ends  of  the 
wire  was  now  126°+  18°,  or  144°;  and  the  force  was 
144  times  as  great  as  that  force  which  would  twist 
the  wire  1°.  But  144  is  four  times  as  great  as  36; 
hence  we  see  that  while  the  distance  had  been  reduced 
to  one  half,  the  force  between  the  balls  had  become 
four  times  as  great.  Had  we  reduced  the  distance 
to  one  quarter,  or  9°,  the  total  torsion  would  have  been 
found  to  be  576°,  or  sixteen  times  as  great;  proving 
the  force  to  vary  inversely  as  the  square  of  the  dis- 
tance. 

In  practice  it  requires  great  experience  and  skill  to 
obtain  results  as  exact  as  this,  for  there  are  many  sources 
of  inaccuracy  in  the  instrument.  The  balls  must  be  very 
small,  in  proportion  to  the  distances  between  them.  The 
charges  of  electricity  on  the  balls  are  found,  moreover,  to 
become  gradually  less  and  less,  as  if  the  electricity  leaked 
away  into  the  air.  This  loss  is  less  if  the  apparatus  be 
quite  dry.  It  is  therefore  usual  to  dry  the  interior  by 
placing  inside  the  case  a  cup  containing  either  chloride 
of  calcium,  or  pumice  stone  soaked  with  strong  sulphuric 
acid,  to  absorb  the  moisture. 

Before  leaving  the  subject  of  electric  forces,  it  may  be 
well  to  mention  that  the  force  of  attraction  between  two 
oppositely  electrified  bodies  varies  also  inversely  as  the 
square  of  the  distance  between  them.  And  in  every 
case,  whether  of  attraction  or  repulsion,  the  force  at  any 
given  distance  is  proportional  to  the  product  of  the  two 
quantities  of  electricity  on  the  bodies.  Thus,  if  we 
had  separately  given  a  charge  of  2  to  the  ball  m  and  a 
charge  of  3  to  the  ball  n,  the  force  between  them  will  be 
3x2  =  6  times  as  great  as  if  each  had  had  a  charge  of  1 
given  to  it.  It  must  be  remembered,  however,  that  the 


CHAP,  i  ELECTRIC   FIELD  23 

law  of  inverse  squares  is  only  true  when  applied  to  the 
case  of  bodies  so  small,  as  compared  with  the  distance 
between  them,  that  they  are  mere  points.  For  flat,  large, 
or  elongated  bodies  the  law  of  inverse  squares  does  not 
hold  good.  The  attraction  between  two  large  flat  disks 
oppositely  electrified  with  given  charges,  and  placed  near 
together,  does  not  vary  with  the  distance. 

20.  Field  between  two    Balls.  —  The   electric   field 
(Art.  13)  between  two  oppositely  electrified  balls  is  found 
to  consist  of  curved  lines. 

By  the  principle  laid  down 
in  Art.  13,  there  is  a  tension 
along  these  lines  so  that 
they  tend  not  only  to  draw 
the  two  balls  together,  but 
also  to  draw  the  electrifica- 
tions on  the  surfaces  of  the 
balls  toward  one  another.  Fi£-  16- 

There  is  also  a  lateral  pressure  in  the  medium  tending  to 
keep  the  electric  lines  apart  from  one  another.  One 
result  of  these  actions  is  that  the  charges  are  no  longer 
equally  distributed  over  the  surfaces,  but  are  more  dense 
on  the  parts  that  approach  most  nearly. 

21.  Unit  Quantity  of  Electricity.  —  In  consequence  of 
these  laws  of  attraction  and  repulsion,  it  is  found  most 
convenient   to    adopt   the  following   definition  for   that 
quantity  of  electricity  which  we  take  for  a  unit  or  stand- 
ard by  which  to  measure  other  quantities  of  electricity. 
One  (electrostatic)  Unit  of  Electricity  is  that  quantity  ivhich, 
when  placed  at  a  distance   of  one   centimetre   in  air  from 
a  similar  and  equal  quantity,  repels  it  with  a  force  of  one 
dyne.     If   instead   of  air  another  medium  occupies  the 
space,  the  force  will  be  different.     For  example,  if  petro- 
leum is  used  the  force  exerted  between  given   charges 
will  be  about  half  as  great  (see  Art.  56).     Further  in- 
formation about  the  measurement  of  electrical  quantities 
is  given  in  Lessons  XXI.  and  XXII. 


24 


ELECTRICITY   AND   MAGNETISM       PART 


LESSON  III.  —  Electrification  ly  Influence 

22.  Influence.  —  We  have  now  learned  how  two 
charged  bodies  may  apparently  attract  or  repel  one 
another.  It  is  sometimes  said  that  it  is  the  charges  in 
the  bodies  which  attract  or  repel  one  another;  but  as 
electrification  is  not  known  to  exist  except  in  or  on 
material  bodies,  the  proof  that  it  is  the  charges  them- 
selves which  are  acted  upon  is  only  indirect.  Nevertheless 
there  are  certain  matters  which  support  this  view,  one  of 


.  IT. 


these  being  the  electric  influence  exerted  by  an  electrified 
body  upon  one  not  electrified. 

Suppose  we  electrify  positively  a  ball  C,  shown  in  Fig. 
17,  and  hold  it  near  to  a  body  that  has  not  been  electri- 
fied, what  will  occur?  We  take  for  this  experiment  the 
apparatus  shown  on  the  right,  consisting  of  a  long  sausage- 
shaped  piece  of  metal,  either  hollow  or  solid,  held  upon  a 
glass  support.  This  "  conductor,"  so  called  because  it  is 
made  of  metal  which  permits  electricity  to  pass  freely 
through  it  or  over  its  surface,  is  supported  on  glass  to 


INFLUENCE  25 


prevent  the  escape  of  electricity  to  the  earth,  glass  being 
a  non-conductor.  The  influence  of  the  positive  charge 
of  the  ball  placed  near  this  conductor  is  found  to  induce 
electrification  on  the  conductor,  which,  although  it  has 
not  been  rubbed  itself,  will  be  found  to  behave  at  its  two 
ends  as  an  electrified  body.  The  ends  of  the  conductor 
will  attract  little  bits  of  paper ;  and  if  pith-balls  be  hung 
to  the  ends  they  are  found  to  be  repelled.  It  will,  how- 
ever, be  found  that  the  middle  region  of  the  long-shaped 
conductor  will  give  no  sign  of  any  electrification.  Further 
examination  will  show  that  the  two  electrifications  on  the 
ends  of  the  conductor  are  of  opposite  kinds,  that  nearest 
the  excited  glass  ball  being  a  negative  charge,  and  that  at 
the  farthest  end  being  an  equal  charge,  but  of  positive 
sign.  It  appears  then  that  a  positive  charge  attracts 
negative  and  repels  positive,  and  that  this  influence  can 
be  exerted  at  a  distance  from  a  body.  If  we  had  begun 
with  a  charge  of  negative  electrification  upon  a  stick  of 
sealing-wax,  the  presence  of  the  negative  charge  near  the 
conductor  would  have  induced  a  positive  charge  on  the 
near  end,  and  negative  on  the  far  end.  This  action, 
discovered  in  1753  by  John  Canton,  is  spoken  of  as 
influence  or  electrostatic  induction.*  It  will  take 
place  across  a  considerable  distance.  Even  if  a  large 
sheet  of  glass  be  placed  between,  the  same  effect  will  be 
produced.  When  the  electrified  body  is  removed  both 
the  charges  disappear  and  leave  no  trace  behind,  and 
the  glass  ball  is  found  to  be  just  as  much  electrified  as 
before;  it  has  parted  with  none  of  its  own  charge.  It 


*  The  word  induction  originally  used  was  intended  to  denote  an  action 
at  a  distance,  as  distinguished  from  conduction,  which  implied  the  convey- 
ance of  the  action  by  a  material  conductor.  But  there  were  discovered 
other  actions  at  a  distance,  namely,  the  induction  of  currents  by  moving 
magnets,  or  by  other  currents,  and  the  induction  of  magnetism  in  iron  in 
the  presence  of  a  neighbouring  magnet.  As  the  term  induction  has  now 
been  officially  adopted  for  the  induction  of  currents,  its  use  in  other  senses 
ought  to  be  dropped.  Hence  the  preference  now  given  to  the  term  influ- 
ence for  the  induction  of  charges  by  charges. 


26 


ELECTRICITY   AND   MAGNETISM        PART  i 


will  be  remembered  that  on  one  theory  a  body  charged 
positively  is  regarded  as  having  more  electricity  than 
the  things  round  it,  while  one  with  a  negative  charge  is 
regarded  as  having  less.  According  to  this  view  it  would 
appear  that  when  a  body  (such  as  the  -f  electrified  glass 
ball)  having  more  electricity  than  things  around  it  is 
placed  near  an  insulated  conductor,  the  uniform  distribu- 
tion of  electricity  in  that  conductor  is  disturbed,  the 
electricity  flowing  away  from  that  end  which  is  near  the 
+  body,  leaving  less  than  usual  at  that  end,  and  producing 

more  than  usual  at  the  other 
end.  This  view  of  things  will 
account  for  the  disappear- 
ance of  all  signs  of  electrifi- 
cation when  the  electrified 
body  is  removed,  for  then 
the  conductor  returns  to  its 
former  condition ;  and  being 
neither  more  nor  less  elec- 


Fig.  IS. 


trifled  than  all  the  objects 
around  on  the  surface  of  the 
earth,  will  show  neither  positive  nor  negative  charge. 
The  action  is  not,  however,  a  mere  action  at  a  distance; 
it  is  one  in  which  the  intervening  medium  takes  an  essen- 
tial part.  Consider  (Fig.  18)  what  takes  place  when  an 
insulated,  non-electrified  metal  ball  B  is  brought  under 
the  influence  of  a  positively  electrified  body  A.  At 
once  some  of  the  electric  lines  of  the  field  that  surrounds 
A  pass  through  B,  entering  it  at  the  side  nearer  A,  and 
leaving  it  at  the  farther  side.  As  the  ball  B  has  no 
charge  of  its  own,  as  many  electric  lines  will  enter  on  one 
side  as  leave  on  the  other;  or,  in  other  words,  the  induced 
negative  charge  on  one  side  and  the  induced  positive 
charge  on  the  other  will  be  exactly  equal  in  amount. 
They  will  not,  however,  be  quite  equally  distributed,  the 
negative  charge  on  the  side  nearer  A  being  more  concen- 
trated, and  the  lines  in  the  field  on  that  side  denser. 


CHAP,  i  ELECTRIC   INFLUENCE  27 

23.  Effects  of  Influence.  —  If  the  conductor  be  made 
in  two  parts,  which  while  under  the  influence  of  the 
electrified  body  are  separated,  then  on  the  removal  of  the 
electrified  body  the  two  charges  can  no  longer  return  to 
neutralize  one  another,  but  remain  each  on  its  own 
portion  of  the  conductor. 

If  the  conductor  be  not  insulated  on  glass  supports, 
but  placed  in  contact  with  the  ground,  that  end  only 
which  is  nearest  the  electrified  body  will  be  found  to 
be  electrified.  The  repelled  charge  is  indeed  repelled  as 
far  as  possible  into  the  walls  of  the  room  ;  or,  if  the 
experiment  be  performed  in  the  open  air,  into  the  earth. 
One  kind  of  electrification  only  is  under  these  circum- 
stances to  be  found,  namely,  the  opposite  kind  to  that 
of  the  excited  body,  whichever  this  may  be.  The  same 
effect  occurs  in  this  case  as  if  an  electrified  body  had  the 
power  of  attracting  up  the  opposite  kind  of  charge  out  of 
the  earth.  < 

The  quantity  of  the  two  charges  thus  separated  by 
influence  on  such  a  conductor  in  the  presence  of  a  charge 
of  electricity,  depends  upon  the  amount  of  the  charge, 
and  upon  the  distance  of  the  charged  body  from  the 
conductor.  A  highly  electrified  glass  rod  will  exert  a 
greater  influence  than  a  less  highly  electrified  one ;  and 
it  produces  a  greater  effect  as  it  is  brought  nearer  and 
nearer.  The  utmost  it  can  do  will  be  to  induce  on  the 
near  end  a  negative  charge  equal  in  amount  to  its  own 
positive  charge,  and  a  similar  amount  of  positive  electri- 
fication at  the  far  end  ;  but  usually,  before  the  electrified 
body  can  be  brought  so  near  as  to  do  this,  something  else 
occurs  which  entirely  alters  the  condition  of  things.  As 
the  electrified  body  is  brought  nearer  and  nearer,  the 
charges  of  opposite  sign  on  the  two  opposed  surfaces 
attract  one  another  more  and  more  strongly  and  accumu- 
late more  and  more  densely,  until,  as  the  electrified  body 
approaches  very  near,  a  spark  is  seen  to  dart  across,  the 
two  charges  thus  rushing  together  to  neutralize  one 


28  ELECTRICITY   AND   MAGNETISM        PART  i 

another,  leaving  the  induced  charge  of  positive  electricity, 
which  was  formerly  repelled  to  the  other  end  of  the 
conductor,  as  a  permanent  charge  after  the  electrified 
body  has  been  removed. 

In  Fig.  19  is  illustrated  the  operation  of  gradually 
lowering  down  over  a  table  a  positively  electrified  metal 
ball.  The  nearer  it  approaches  the  table,  the  more  does 
the  electric  field  surrounding  it  concentrate  itself  in  the 
gap  between  the  ball  and  the 
table  top;  the  latter  becoming 
negatively  electrified  by  influ- 
ence. Where  the  electric  lines 
are  densest  the  tension  in  the 
medium  is  greatest,  until  when 
the  ball  is  lowered  still  further 
the  mechanical  resistance  of  the 
air  can  no  longer  withstand 
Fio.  19  the  stress;  it  breaks  down  and 

the  layer  of  air  is  pierced  by  a 
spark.  If  oil  is  used  as  a  surrounding  medium  instead  of 
air,  it  will  be  found  to  stand  a  much  greater  stress  without 
being  pierced. 

24.  Attraction  due  to  Influence.  —  We  are  now  able 
to  apply  the  principle  of  influence  to  explain  why  an 
electrified  body  should  attract  things  that  have  not  been 
electrified  at  all.  Fig.  18,  on  p.  26,  may  be  taken  to 
represent  a  light  metal  ball  B  hung  from  a  silk  thread 
presented  to  the  end  of  a  rubbed  glass  rod  A.  The 
positive  charge  on  A  produces  l>y  influence  a  negative 
charge  on  the  nearer  side  of  B  and  an  equal  positive 
charge  on  the  far  side  of  B.  The  nearer  half  of  the  ball 
will  therefore  be  attracted,  and  the  farther  half  repelled ; 
but  the  attraction  will  be  stronger  than  the  repulsion, 
because  the  attracted  charge  is  nearer  than  the  repelled. 
Hence  on  the  whole  the  ball  will  be  attracted.  It  can 
easily  be  observed  that  if  a  ball  of  non-conducting 
substance,  such  as  wax,  be  employed,  it  is  not  attracted 


CEIAP.  i  THE   ELECTROPHORUS  29 

so  much  as  a  ball  of  conducting  material.     This  in  itself 
proves  that  influence  really  precedes  attraction. 

Another  way  of  stating  the  facts  is  as  follows  :  —  The 
tension  along  the  electric  field  on  the  right  of  B  will  be 
greater  than  that  on  the  left,  because  of  the  greater 
concentration  of  the  electric  lines  on  the  right. 

25.  Dielectric  Power.  —  We  have  pointed  out  several 
times  what  part  the  intervening  medium  plays  in  these 
actions  at  a  distance.   The  air,  oil,  glass,  or  other  material 
between  does  not  act  simply  as  a  non-conductor ;  it  takes 
part  in  the  propagation  of  the  electric  forces.      Hence 
Faraday,  who  discovered  this  fact,  termed  such  materials 
dielectrics.     Had  oil,  or  solid  sulphur,  or  glass  been  used 
instead  of  air,  the  influence  exerted  by  the  presence  of  the 
electrified  body  at  the  same  distance  would   have  been 
greater.      The  power  of  a  non-conducting  substance  to 
convey  the  influence  of   an  electrified  body  across  it  is 
called  its   dielectric  power  (or   was  formerly  called   its 
specific  inductive  capacity,  see  Art.  56  and  Lesson  XXIII.). 

26.  The  Electrophorus.  —  We  are  now  prepared  to 
explain  the  operation  of  a  simple  and  ingenious  instru- 
ment,  devised   by  Volta  in    1775,   for  the  purpose   of 
procuring,  by  the  principle   of   influence,  an  unlimited 
number  of  charges  of  electricity  from  one  single  charge. 
This  instrument*   is   the  Electrophorus   (Fig.  20).      It 
consists  of  two  parts,  a  round  cake  of  resinous  material 
cast  in   a  metal   dish   or   "sole,"   about    12    inches   in 
diameter,  and  a  round  disk  of  slightly  smaller  diameter 
made  of   metal,  or   of  wood  covered  with  tinfoil,  and 
provided  with  a  glass  handle.     Shellac,  or  sealing-wax,  or 
a  mixture  of  resin,  shellac,  and  Venice  turpentine,  may 
be  used  to  make  the  cake.     A  slab  of  sulphur  will  also 
answer,  but  it  is  liable  to  crack.     Sheets  of  hard  ebonized 
indiarubber  are  excellent ;  but  the  surface  of  this  substance 

*  Volta's  electrophorus  was  announced  IB  1775.  Its  principle  had 
already  been  anticipated  by  Wilcke,  who  in  1762  described  to  the  Swedish 
Academy  of  Sciences  two  "  charging-machines  "  working  by  influence. 


30 


ELECTRICITY   AND    MAGNETISM       PART  i 


requires  occasional  washing  with  ammonia  and  rubbing 
with  paraffin  oil,  as  the  sulphur  contained  in  it  is  liable 
to  oxidize  and  to  attract  moisture.  To  use  the  electro- 
phorus  the  resinous  cake  must  be  beaten  or  rubbed  with 
a  warm  piece  of  woollen  cloth,  or,  better  still,  with  a  cat's 


Fig.  20. 

skin.  The  disk  or  "  cover  "  is  then  placed  upon  the  cake, 
touched  momentarily  with  the  finger,  then  removed  by 
taking  it  up  by  the  glass  handle,  when  it  is  found  to  be 
powerfully  electrified  with  a  positive  charge,  so  much  so 
indeed  as  to  yield  a  spark  when  the  knuckle  is  presented 
to  it.  The  "  cover  "  may  be  replaced,  touched,  and  once 
more  removed,  and  will  thus  yield  any  number  of  sparks, 


CHAP,  i  THE   ELECTROPHORUS  31 

the   original  charge   on   the  resinous    plate    meanwhile 
remaining  practically  as  strong  as  before. 

The  theory  of  the  electrophorus  is  very  simple,  pro- 
vided the  student  has  clearly  grasped  the  principle  of 
influence  explained  above.  When  the  resinous  cake  is 
first  beaten  with  the  cat's  skin  its  surface  is  negatively 
electrified,  as  indicated  in  Fig.  21.  When  the  metal  disk 
is  placed  down  upon  it,  it  rests  really  only  on  three  or 
four  points  of  the  surface,  and  may  be  regarded  as  an 
insulated  conductor  in  the  presence  of  an  electrified  body. 
The  negative  electrification  of  the  cake  therefore  acts  by 
influence  on  the  metallic  disk  or  "  cover,"  the  natural 
electricity  in  it  being  displaced  downwards,  producing  a 
positive  charge  on  the  under  side,  and  leaving  the  upper 


r 


Fig.  21.  Fig.  22. 

side  negatively  electrified.  This  state  of  things  is  shown 
in  Fig.  22.  If  now  the  cover  be  touched  for  an  instant 
with  the  finger,  the  negative  charge  of  the  upper  surface 
will  be  neutralized  by  electricity  flowing  in  from  the  earth 
through  the  hand  and  body  of  the  experimenter.  The 
attracted  positive  charge  will,  however,  remain,  being 
bound  as  it  were  by  its  attraction  towards  the  negative 
charge  on  the  cake.  Fig.  23  shows  the  condition  of 
things  after  the  cover  has  been  touched.  If,  finally,  the 
cover  be  lifted  by  its  handle,  the  remaining  positive 
charge  will  be  no  longer  "  bound  "  on  the  lower  surface 
by  attraction,  but  will  distribute  itself  on  both  sides  of 
the  cover,  and  may  be  used  to  give  a  spark,  as  already 
said.  It  is  clear  that  no  part  of  the  original  charge  has 
been  consumed  in  the  process,  which  may  be  repeated  as 


ELECTRICITY   AND   MAGNETISM        PAKT  i 

often  as  desired.  As  a  matter  of  fact,  the  charge  on  the 
cake  slowly  dissipates  —  especially  if  the  air  be  damp. 
Hence  it  is  needful  sometimes  to  renew  the  original  charge 
by  afresh  beating  the  cake  with  the  cat's  skin.  The 
labour  of  touching  the  cover  with  the  finger  at  each 
operation  may  be  saved  by  having  a  pin  of  brass  or  a 
strip  of  tinfoil  projecting  from  the  metallic  "  sole  "  on  to 
the  top  of  the  cake,  so  that  it  touches  the  plate  each  time, 
and  thus  neutralizes  the  negative  charge  by  allowing 
electricity  to  flow  in  from  the  earth. 

The    principle    of    the    electrophorus    may   then    be 
summed  up  in  the  following  sentence.     A   conductor  if 


i"  f  TT 


Fig.  23.  Fig.  24. 

touched  while  under  the  influence  of  a  charged  body  acquires 
thereby  a  charge  of  opposite  sign.* 

Since  the  electricity  thus  yielded  by  the  electro- 
phorus is  not  obtained  at  the  expense  of  any  part  of  the 
original  charge,  it  is  a  matter  of  some  interest  to  inquire 
what  the  source  is  from  which  the  energy  of  this  apparently 
unlimited  supply  is  drawn ;  for  it  cannot  be  called  into 

*  Priestley,  in  1767,  stated  this  principle  in  the  following  language  :  — 
"  The  electric  fluid,  when  there  is  a  redundancy  of  it  in  any  body,  repels 
the  electric  fluid  in  any  other  body,  when  they  are  brought  within  the 
sphere  of  each  other's  influence,  and  drives  it  into  the  remote  parts  of  the 
body ;  or  quite  out  of  the  body,  if  there  be  any  outlet  for  that  purpose. 
In  other  words,  bodies  immerged  in  electric  atmospheres  always  become 
possessed  of  the  electricity,  contrary  to  that  of  the  body,  in  whose  atmo- 
sphere they  are  immerged." 


CHAF.  i        FREE   AND   BOUND   CHARGES  33 

existence  without  the  expenditure  of  some  other  form  of 
energy,  any  more  than  a  steam-engine  can  work  without 
fuel.  As  a  matter  of  fact  it  is  found  that  it  is  a  little 
harder  work  to  lift  up  the  cover  when  it  is  charged  than 
if  it  were  not  charged;  for,  when  charged,  there  is  the 
tension  of  the  electric  field  to  be  overcome  as  well  as  the 
force  of  gravity.  Slightly  harder  work  is  done  at  the  ex- 
pense  of  the  muscular  energies  of  the  operator ;  and  this 
is  the  real  origin  of  the  energy  stored  up  in  the  separate 
charges.  The  purely  mechanical  actions  of  putting  down 
the  disk  on  the  cake,  touching  it,  and  lifting  it  up, 
can  be  performed  automatically  by  suitable  mechanical 
arrangements,  which  render  the  production  of  these 
inductive  charges  practically  continuous.  Of  such  con- 
tinuous electrophori,  the  latest  is  Wimshurst's  machine, 
described  in  Lesson  V. 

27.  "Free"  and  "Bound"  Electrification.  —  We 
have  spoken  of  a  charge  of  electricity  on  the  surface  of  a 
conductor,  as  being  "  bound  "  when  it  is  attracted  by  the 
presence  of  a  neighbouring  charge  of  the  opposite  kind. 
The  converse  term  "  free  "  is  sometimes  applied  to  the 
ordinary  state  of  electricity  upon  a  charged  conductor, 
not  in  the  presence  of  a  charge  of  an  opposite  kind.  A 
"  free  "  charge  upon  an  insulated  conductor  flows  away 
instantaneously  to  the  earth,  if  a  conducting  channel  be 
provided,  as  will  be  explained.  It  is  immaterial  what 
point  of  the  conductor  be  touched.  Thus,  in  the  case 
represented  in  Fig.  17,  wherein  a  +  electrified  body 
induces  —  electrification  at  the  near  end,  and  +  electri- 
fication at  the  far  end  of  an  insulated  conductor,  the  — 
charge  is  "  bound,"  being  attracted,  while  the  -f-  charge 
at  the  other  end,  being  repelled,  is  "  free  " ;  and  if  the 
insulated  conductor  be  touched  by  a  person  standing  on  the 
ground,  the  "free"  charge  will  flow  away  through  his  body 
to  the  earth,  or  to  the  walls  of  the  room,  while  the  "  bound  " 
charge  will  remain,  no  matter  whether  he  touch  the  con- 
ductor at  the  far  end,  or  at  the  near  end,  or  at  the  middle. 


34  ELECTRICITY   AND   MAGNETISM        PAKT  i 

28.  Method  of  charging   the   Gold-Leaf  Electroscope 
by   Influence.  —  The   student  will  now   be  prepared  to 
understand  the  method  by  which  a  Gold-Leaf   Electro- 
scope can  be  charged  with  the  opposite  kind  of  charge  to 
that  of  the  electrified  body  used  to  charge  it.     In  Lesson 
IT.  it  was  assumed  that  the  way  to  charge  an  electroscope 
was  to  place  the  excited  body  in  contact  with  the  knob, 
and  thus  permit,  as  it  were,  a  small  portion  of  the  charge 
to  flow  into  the  gold  leaves.     A  rod  of  glass  rubbed  on 
silk  being  -f  would  thus  obviously  impart  +  electrifica- 
tion to  the  gold  leaves. 

Suppose,  however,  the  rubbed  glass  rod  to  be  held  a 
few  inches  above  the  knob  of  the  electroscope,  as  is 
indeed  shown  in  Fig.  12.  Even  at  this  distance  the  gold 
leaves  diverge,  and  the  effect  is  due  to  influence.  The 
gold  leaves,  and  the  brass  wire  and  knob,  form  one  con- 
tinuous conductor,  insulated  from  the  ground  by  the 
glass  jar.  The  presence  of  the  +  charge  of  the  glass  acts 
inductively  on  this  "insulated  conductor,"  inducing  — 
electrification  on  the  near  end  or  knob,  and  inducing  + 
at  the  far  end,  i.e.  on  the  gold  leaves,  which  diverge. 
Of  these  two  induced  charges,  the  —  on  the  knob  is 
"  bound,"  while  the  +  on  the  leaves  is  "  free."  If  now, 
while  the  excited  rod  is  still  held  above  the  electroscope, 
the  knob  be  touched  by  a  person  standing  on  the  ground, 
one  of  these  two  induced  charges  flows  to  the  ground, 
namely,  the  free  charge  —  not  that  on  the  knob  itself,  for 
it  was  "bound,"  but  that  on  the  gold  leaves  which  was 
"free" —  and  the  gold  leaves  instantly  drop  down  straight. 
There  now  remains  only  the  —  charge  on  the  knob, 
"  bound "  so  long  as  the  -f-  charge  of  the  glass  rod  is 
near  to  attract  it.  But  if,  finally,  the  glass  rod  be  taken 
right  away,  the  —  charge  is  no  longer  "  bound  "  on  the 
knob,  but  is  "  free  "  to  flow  into  the  leaves,  which  once 
more  diverge — but  this  time  with  a  negative  electrification. 

29.  The  "Return-Shock."  —  It  is  sometimes  noticed 
that,  when  a  charged  conductor  is  suddenly  discharged, 


CONDUCTION  35 


a  discharge  is  felt  by  persons  standing  near,  or  may 
even  affect  electroscopes,  or  yield  sparks.  This  action, 
known  as  the  "return-shock,"  is  due  to  influence.  For 
in  the  presence  of  a  charged  conductor  a  charge  of 
opposite  sign  will  be  induced  in  neighbouring  bodies, 
and  on  the  discharge  of  the  conductor  these  neighbour- 
ing bodies  may  also  suddenly  discharge  their  induced 
charge  into  the  earth,  or  into  other  conducting  bodies. 
A  "return-shock"  is  sometimes  felt  by  persons  standing 
on  the  ground  at  the  moment  when  a  flash  of  lightning 
has  struck  an  object  some  distance  away. 


LESSON  IV.  —  Conduction  and   Distribution  of  Electricity 

SO.  Conduction.  —  Toward  the  close  of  Lesson  I.  we 
explained  how  certain  bodies,  such  as  the  rnetals,  conduct 
electricity,  while  others  are  non-conductors  or  insulators. 
This  discovery  is  due  to  Stephen  Gray ;  who,  in  1729, 
found  that  a  cork,  inserted  into  the  end  of  a  rubbed  glass 
tube,  and  even  a  rod  of  wood  stuck  into  the  cork,  pos- 
sessed the  power  of  attracting  light  bodies.  He  found, 
similarly,  that  metallic  wire  and  pack-thread  conducted 
electricity,  while  silk  did  not. 

We  may  repeat  these  experiments  by  taking  (as  in 
Fig.  25)  a  glass  rod,  fitted  with  a  cork  and  a  piece  of 
wood.  If  a  bullet  or  a  brass  knob  be  hung  to  the  end  of 
this  by  a  linen  thread  or  a  wire,  it  is  found  that  when  the 
glass  tube  is  rubbed  the  bullet  acquires  the  property  of 
attracting  light  bodies.  If  a  dry  silk  thread  is  used, 
however,  no  electricity  will  flow  down  to  the  bullet. 

Gray  even  succeeded  in  transmitting  a  charge  of 
electricity  through  a  hempen  thread  over  700  feet  long, 
suspended  on  silken  loops.  A  little  later  Du  Fay 
succeeded  in  sending  electricity  to  no  less  a  distance 
than  1250  feet  through  a  moistened  thread,  thus  proving 
the  conducting  power  of  moisture.  From  that  time  the 


ELECTRICITY   AND   MAGNETISM       TART  i 


classification  of  bodies  into  conductors  and  insulators  has 
been  observed. 

This  distinction  cannot,  however,  be  entirely  main- 
tained, as  a  large  class  of  substances  occupy  an  inter- 
mediate ground  as  partial  conductors.  For  example,  dry 
wood  is  a  bad  conductor  and  also  a  bad  insulator  ;  it 
is  a  good  enough  conductor  to  conduct  away  the  high- 
potential  electricity  obtained  by  friction,  but  it  is  a 
bad  conductor  for  the  relatively  low-potential  electricity 
of  small  voltaic  batteries.  Substances  that  are  very  bad 


Fig.  25. 

conductors  are  said  to  offer  a  great  resistance  to  the 
flow  of  electricity  through  them.  There  is  indeed  no 
substance  so  good  a  conductor  as  to  be  devoid  of  resist- 
ance. There  is  no  substance  of  so  high  a  resistance  as 
not  to  conduct  a  little.  Even  silver,  which  conducts  best 
of  all  known  substances,  resists  the  flow  of  electricity  to 
a  small  extent ;  and,  on  the  other  hand,  such  a  non-con- 
ducting substance  as  glass,  though  its  resistance  is  many 
million  times  greater  than  any  metal,  does  allow  a  very 
small  quantity  of  electricity  to  pass  through  it.  In  the 


CHAP.    I 


CONDUCTORS 


37 


following  list,  the  substances  named  are  placed  in.  order, 
each  conducting  better  than  those  lower  down  on  the  list. 


Silver    .    . 
Copper  .    . 
Other  metals 
Charcoal    . 
Water    .     . 


Good  Conductors. 


The  body  .     .    1 

Cotton  ... 

Dry  wood  .     .    [  Partial  Conductors. 

Marble  .     .     . 

Paper    .    .     .    J 


Oils  .  .  . 
Porcelain  . 
Wool  .  . 
Silk  .  .  . 
Resin  .  . 
Guttapercha 
Shellac  .  . 
Ebonite  . 
Paraffin  . 
Glass  .  . 
Quartz  (fused) 
Air  . 


Non-Conductors  or 
Insulators. 


A  simple  way  of  observing  experimentally  whether  a 
body  is  a  conductor  or  not,  is  to  take  a  charged  gold- 
leaf  electroscope,  and,  holding  the  substance  to  be 
examined  in  the  hand,  touch  the  knob  of  the  electro- 
scope with  it.  If  the  substance  is  a  conductor  the  elec- 
tricity will  flow  away  through  it  and  through  the  body 
to  the  earth,  and  the  electroscope  will  be  discharged. 
Through  good  conductors  the  rapidity  of  the  flow  is  so 
great  that  the  discharge  is  practically  instantaneous. 
Further  information  on  this  question  is  given  in  Lesson 
XXXIII. 

31.  Distribution  of  Charge  on  Bodies.  —  If  electri- 
fication is  produced  at  one  part  of  a  non-conducting 
body,  it  remains  at  that  point  and  does  not  flow  over 
the  surface,  or  at  most  flows  over  it  excessively  slowly. 


38  ELECTRICITY  AND   MAGNETISM       PART  i 

Thus  if  a  glass  tube  is  rubbed  at  one  end,  only  that  one 
end  is  electrified.  Hot  glass  is,  however,  a  conductor. 
If  a  warm  cake  of  resin  be  rubbed  at  one  part  with  a 
piece  of  cloth,  only  the  portion  rubbed  will  attract  light 
bodies,  as  may  be  proved  by  dusting  upon  it  through 
a  piece  of  muslin  fine  powders  such  as  red  lead,  lyco- 
podium,  or  verdigris,  which  adhere  where  the  surface  is 
electrified.  The  case  is,  however,  wholly  different  when 
a  charge  of  electricity  is  imparted  to  any  part  of  a  con- 
ducting body  placed  on  an  insulating  support,  for  it 
instantly  distributes  itself  all  over  the  surface,  though  in 
general  not  uniformly  over  all  points  of  the  surface. 

32.  The  Charge  resides  on  the  Surface.  —  A  charge 
of  electricity  resides  only  on  the  surface  of  conducting 
bodies.  This  is  proved  by  the  fact  that  it  is  found 
to  be  immaterial  to  the  distribution  what  the  inte- 
rior of  a  conductor  is  made  of;  it  may  be  solid  metal, 
or  hollow,  or  even  consist  of  wood  covered  with  tinfoil 
or  gilt,  but,  if  the  shape  be  the  same,  the  charge  will 
distribute  itself  precisely  in  the  same  manner  over  the 
surface.  There  are  also  several  ways  of  proving  by 
direct  experiment  this  very  important  fact.  Let  a  hollow 
metal  ball,  having  an  aperture  at  the  top,  be  taken  (as  in 
Fig.  26),  and  set  upon  an  insulating  stem,  and  charged 
by  sending  into  it  a  few  sparks  from  an  electrophorus. 
The  absence  of  any  charge  in  the  interior  may  be  shown 
as  follows:  —  In  order  to  observe  the  nature  of  the  elec- 
trification of  a  charged  body,  it  is  convenient  to  have  some 
means  of  removing  a  small  quantity  of  the  charge  as 
a  sample  for  examination.  To  obtain  such  a  sample,  a 
little  instrument  known  as  a  proof-plane  is  employed. 
It  consists  of  a  little  disk  of  sheet  copper  or  of  gilt  paper 
fixed  at  the  end  of  a  small  glass  rod.  If  this  disk  is  laid 
on  the  surface  of  an  electrified  body  at  any  point,  part 
of  the  charge  flows  into  it,  and  it  may  be  then  removed, 
and  the  sample  thus  obtained  may  be  examined  with  a 
gold-leaf  electroscope  in  the  ordinary  way.  For  some 


CIIA.P.    I 


CHARGE   ON  SURFACE 


39 


purposes  a  metallic  bead,  fastened  to  the  end  of  a  glass 
rod,  is  more  convenient  than  a  flat  disk.  If  such  a  proof- 
plane  be  applied  to  the  outside  of  our  electrified  hollow 
ball,  and  then  touched  on  the  knob  of  an  electroscope, 
the  gold  leaves  will  diverge,  showing  the  presence  of  a 


Fig.  26. 

charge.  But  if  the  proof-plane  be  carefully  inserted 
through  the  opening,  and  touched  against  the  inside  of 
the  globe  and  then  withdrawn,  it  will  be  found  that 
the  inside  is  destitute  of  electrification.  An  electrified 
pewter  mug  will  show  a  similar  result,  and  so  will  even 
a  cylinder  of  gauze  wire. 


40 


ELECTRICITY   AND    MAGNETISM        PART  i 


33.  Blot's  Experiment.  —  Biot  proved  the  same  fact 
in  another  way.  A  copper  ball  was  electrified  and 
insulated.  Two  hollow  hemispheres  of  copper,  of  a 
larger  size,  and  furnished  with  glass  handles,  were  then 
placed  together  outside  it  (Fig.  27).  So  long  as  they 
did  not  come  into  contact  the  charge  remained  on  the 
inner  sphere ;  but  if  the  outer  shell  touched  the  inner 
sphere  for  but  an  instant,  the  whole  of  the  charge  passed 


A 


&g.  2T. 

to  the  exterior  ;  and  when  the  hemispheres  were  separated 
and  removed  the  inner  globe  was  found  to  be  completely 
discharged. 

34.  Further  Explanation.  —  Doubtless  the  explana- 
tion of  this  behaviour  of  electricity  is  to  be  found  in  the 
property  previously  noticed  as  possessed  by  either  kind 
of  electrification,  namely,  that  of  repelling  itself ;  hence 
it  retreats  as  far  as  can  be  from  the  centre  and  remains 
upon  the  surface.  An  important  proposition  concerning 
the  absence  of  electric  force  within  a  closed  conductor  is 
proved  in  Lesson  XXI. ;  meanwhile  it  must  be  noted  that 
the  proofs,  so  far,  are  directed  to  demonstrate  the  absence 


CHAP,  i       ELECTRIFICATION  EXTERNAL  41 

of  a  free  charge  of  electricity  in  the  interior  of  hollow  con- 
ductors. Amongst  other  experiments,  Terqueni  showed 
that  a  pair  of  gold  leaves  hung  inside  a  wire  cage  could 
not  be  made  to  diverge  when  the  cage  was  electrified. 
Faraday  constructed  a  conical  bag  of  linen-gauze,  sup- 
ported as  in  Fig.  28,  upon  an  insulating  stand,  and  to 
which  silk  strings  were  attached,  by  which  it  could  be 
turned  inside  out.  It  was  charged,  and  the  charge  was 
shown  by  the  proof -plane  and  electroscope  to  be  on  the 
outside  of  the  bag.  On  turning  it  inside  out  the  elec- 


Fig.  28. 

tricity  was  once  more  found  outside.  Faraday's  most 
striking  experiment  was  made  with  a  hollow  cube, 
measuring  12  feet  each  way,  built  of  wood,  covered  with 
tinfoil,  insulated,  and  charged  with  a  powerful  machine, 
so  that  large  sparks  and  brushes  were  darting  off  from 
every  part  of  its  outer  surface.  Into  this  cube  Faraday 
took  his  most  delicate  electroscopes ;  but  once  within  he 
failed  to  detect  the  least  effect  upon  them. 

35.   Applications.  —  Advantage  is  taken   of  this   in 
the    construction    of  delicate    electrometers   and    other 


42  ELECTRICITY   AND   MAGNETISM        PART  j 

instruments,  which  can  be  effectually  screened  from 
the  influence  of  electrified  bodies  by  enclosing  them 
in  a  cover  of  thin  metal,  closed  all  round,  except  where 
apertures  must  be  made  for  purposes  of  observation. 
Metal  gauze  answers  excellently,  and  is  nearly  trans- 
parent. It  was  proposed  by  the  late  Professor  Clerk 
Maxwell  to  protect  buildings  from  lightning  by  covering 
them  on  the  exterior  with  a  network  of  wires. 

36.  Apparent  Exceptions.  —  There  are  two  apparent 
exceptions  to  the  law  that  electrification  resides  only  on 
the   outside  of  conductors.     (1)  If  there  are  electrified 
insulated   bodies  actually  placed  inside  the  hollow  con- 
ductor,   the  presence    of    these    electrified    bodies    acts 
inductively  and  attracts  the  opposite  kind  of  charge  to 
the  inner  side  of  the  hollow  conductor.     (2)  When  elec- 
tricity flows  in  a  current,  it  flows  through  the  substance 
of  the   conductor.      The    law  is    limited    therefore    to 
electricity  at  rest,  —  that  is,  to  statical  charges. 

37.  Faraday's  "  Ice-pail  "  Experiment.  —  One  experi- 
ment of  Faraday  deserves  notice,  as  showing  the  part 
played  by  induction  in  these  phenomena.     He  gradually 
lowered  a  charged  metallic  ball  into  a  hollow  conductor 
connected  by  a  wire  to  a  gold-leaf  electroscope  (Fig.  29), 
and  watched  the  effect.     A  pewter  ice-pail    being  con- 
venient  for   his  purpose,  this  experiment  is  continually 
referred  to  by  this  name,  though  any  other  hollow  con- 
ductor—  a  tin   canister  or   a  silver   mug,  placed  on   a 
glass   support  —  would   of  course   answer   equally  well. 
The  following  effects  are  observed :  — Suppose  the  ball 
to  have  a  +  charge :  as  it  is  lowered  into  the  hollow  con- 
ductor the  gold  leaves  begin  to  diverge,  for  the  presence 
of  the  charge  acts  inductively,  and  attracts  a  —  charge 
into  the  interior  and  repels  a  +  charge  to  the  exterior. 
The  gold   leaves  diverge  more  and  more  until   the  ball 
is   right  within    the   hollow   conductor,  after   which   no 
greater   divergence    is   obtained.     On    letting  the    ball 
touch  the  inside  the  gold  leaves  still  remain  diverging1  as 


CHAP.    I 


DISTRIBUTION   OF   CHARGE 


43 


before,  and  if  now  the  ball  is  pulled  out  it  is  found  to 
have  lost  all  its  electrification.  The  fact  that  the  gold 
leaves  diverge  no  wider  after  the  ball  touched  than  they 
did  just  before,  proves 
that  when  the  charged 
ball  is  right  inside  the 
hollow  conductor  the 
induced  charges  are 
each  of  them  precisely 
equal  in  amount  to  its 
own  charge,  and  the  in- 
terior negative  charge 
exactly  neutralizes  the 
charge  on  the  ball  at 
the  moment  when  they 
touch,  leaving  the 
equal  exterior  charge 
unchanged.  An  electric 
cage,  such  as  this  ice- 
pail,  when  connected 
with  an  electroscope 
or  electrometer,  affords  an  excellent  means  of  examining 
the  charge  on  a  body  small  enough  to  be  hung  inside 
it.  For  without  using  up  any  of  the  charge  of  the  body 
(which  we  are  obliged  to  do  when  applying  the  method 
of  the  proof-plane)  we  can  examine  the  induced  charge 
repelled  to  the  outside  of  the  cage,  which  is  equal  in 
amount  and  of  the  same  sign.  If  two  equal  charges  of 
opposite  kinds  are  placed  at  the  same  time  within  the 
cage  no  effects  are  produced  on  the  outside. 

38.  Distribution  of  Charge.  —  A  charge  of  electricity 
is  not  usually  distributed  uniformly  over  the  surfaces 
of  bodies.  Experiment  shows  that  there  is  more  elec- 
tricity on  the  edges  and  corners  of  bodies  than  upon 
their  flatter  parts.  This  distribution  can  be  deduced 
from  the  theory  laid  down  in  Lesson  XXI.,  but  mean- 
time we  will  give  some  of  the  chief  cases  as  they  can  be 


Fig.  29. 


44  ELECTRICITY   AND   MAGNETISM        PART  i 

shown  to  exist.  The  term  Electric  Density  is  used  to 
signify  the  amount  of  electricity  at  any  point  of  a  sur- 
face ;  the  electric  density  at  a  point  is  the  number  of  units 
of  electricity  per  unit  of  area  (i.e.  per  square  inch,  or  per 
square  centimetre),  the  distribution  being  supposed  uni- 
form over  this  small  surface. 

(a)  Sphere.  —  The  distribution  of  a  charge  over  an 
insulated  sphere  of  conducting  material  is  uniform,  pro- 
vided the  sphere  is  also  isolated,  that  is  to  say,  is  remote 
from  the  presence  of  all  other  conductors  and  all  other 
electrified  bodies.  The  density  is  uniform  all  over  it. 
This  is  symbolized  by  the  dotted  line  round  the  sphere 


Fig.  30. 

in  Fig.  30  a,  which  is  at  an  equal  distance  from  the 
sphere  all  round,  suggesting  an  equal  thickness  of  charge 
at  every  point  of  the  surface.  It  must  be  remembered 
that  the  charge  is  not  really  of  any  perceptible  thickness 
at  all ;  it  resides  on  or  at  the  surface,  but  cannot  be  said 
to  form  a  stratum  upon  it. 

(6)  Cylinder  with  rounded  Ends.  — Upon  an  elongated 
conductor,  such  as  is  frequently  employed  in  electrical 
apparatus,  the  density  is  greatest  at  the  ends  where  the 
curvature  of  the  surface  is  the  greatest. 

(c)  Two  Spheres  in  contact.  —  If  two  spheres  in  con- 
tact with  each  other  are  insulated  and  charged,  it  is  found 
that  the  density  is  greatest  at  the  parts  farthest  from  the 


CHAP,  i  DISTRIBUTION   OF   CHARGE  45 

point  of  contact,  and  least  in  the  crevice  between  them. 
If  the  spheres  are  of  unequal  sizes  the  density  is  greater 
on  the  smaller  sphere,  which  has  the  surface  more  curved. 
On  an  egg-shaped  or  pear-shaped  conductor  the  density 
is  greatest  at  the  small  end.  On  a  cone  the  density  is 
greatest  at  the  apex  ;  and  if  the  cone  terminate  in  a 
sharp  point  the  density  there  is  very  much  greater  than 
at  any  other  point.  At  a  point,  indeed,  the  density  of 
the  collected  electricity  may  be  so  great  as  to  electrify 
the  neighbouring  particles  of  air,  which  then  are  repelled 
(see  Art.  47),  thus  producing  a  continual  loss  of  charge. 
For  this  reason  points  and  sharp  edges  are  always  avoided 
on  electrical  apparatus,  except  where  it  is  specially  desired 
to  set  up  a  discharge. 

(d)  Flat  Disk.  —  The  density  of  a  charge  upon  a  flat 
disk  is  greater,  as  we  should  expect,  at  the  edges  than  on 
the  flat  surfaces ;  but  over  the  flat  surfaces  the  distribu- 
tion is  fairly  uniform. 

These  various  facts  are  ascertained  by  applying  a 
small  proof-plane  successively  at  various  points  of  the 
electrified  bodies  and  examining  the  amount  taken  up  by 
the  proof-plane  by  means  of  an  electroscope  or  electrome- 
ter. Coulomb,  who  investigated  mathematically  as  well 
as  experimentally  many  of  the  important  cases  of  distri- 
bution, employed  the  torsion  balance  to  verify  his  calcu- 
lations. He  investigated  thus  the  case  of  the  ellipsoid  of 
revolution,  and  found  the  densities  of  the  charges  at  the 
extremities  of  the  axis  to  be  proportional  to  the  lengths 
of  those  axes.  He  also  showed  that  the  density  of  the 
charge  at  any  other  point  of  the  surface  of  the  ellipsoid 
was  proportional  to  the  length  of  the  perpendicular  drawn 
from  the  centre  to  the  tangent  at  that  point.  Riess  also 
investigated  several  interesting  cases  of  distribution.  He 
found  the  density  at  the  middle  of  the  edges  of  a  cube  to 
be  nearly  two  and  a  half  times  as  great  as  the  density  at 
the  middle  of  a  face ;  while  the  density  at  a  corner  of  the 
cube  was  more  than  four  times  as  great. 


46  ELECTRICITY   AND   MAGNETISM        PART  i 

39.  Redistribution  of  Charge.  — If  any  portion  of  the 
charge  of  an  insulated  conductor   be   removed,  the  re- 
mainder of  the  charge  will  immediately  redistribute  itself 
over  the   surface  in   the  same   manner  as    the    original 
charge,  provided  it  be  also  isolated,  i.e.  that  no  other  con- 
ductors or  charged  bodies  be  near  to  perturb  the  distri- 
bution by  complicated  effects  of  influence. 

If  a  conductor  be  charged  with  any  quantity  of  elec- 
tricity, and  another  conductor  of  the  same  size  and  shape 
(but  uncharged)  be  brought  into  contact  with  it  for  an 
instant  and  then  separated,  it  will  be  found  that  the 
charge  has  divided  itself  equally  between  them.  In  the 
same  way  a  charge  may  be  divided  equally  into  three 
or  more  parts  by  being  distributed  simultaneously  over 
three  or  more  equal  and  similar  conductors  brought  into 
contact  and  symmetrically  placed. 

If  two  equal  metal  balls,  suspended  by  silk  strings, 
charged  with  unequal  quantities  of  electricity,  are  brought 
for  an  instant  into  contact  and  then  separated,  it  will  be 
found  that  the  charge  has  redistributed  itself  fairly,  half 
the  sum  of  the  two  charges  being  now  the  charge  of  each. 
This  may  even  be  extended  to  the  case  of  charges  of 
opposite  signs.  Thus,  supple  two  similar  conductors  to 
be  electrified,  one  with  a  positive  charge  of  5  units  and 
the  other  with  3  units  of  negative  charge,  when  these  are 
made  to  touch  and  separated,  each  will  have  a  positive 
charge  of  1  unit ;  for  the  algebraic  sum  of  +  5  and  —  3  is 
-f  2,  which,  shared  between  the  two  equal  conductors, 
leaves  +  1  for  each. 

40.  Capacity  of  Conductors.  —  If  the  conductors  be 
unequal  in  size,  or  unlike  in  form,  the  shares  taken  by 
each  in  this  redistribution  will  not  be  equal,  but  will  be 
proportional  to  the  electric  capacities  of  the  conductors. 
The   definition   of    capacity   in   its   relation   to   electric 
quantities  is  given  in  Lesson  XXL,  Art.  271.     We  may, 
however,  make  the  remark,  that  two  insulated  conductors 
of  the  same  form,  but  of  different  sizes,  differ  in  their 


CHAP,  i  ELECTRIC   MACHINES  47 

electrical  capacity ;  for  the  larger  one  must  have  a  larger 
amount  of  electricity  imparted  to  it  in  order  to  electrify 
its  surface  to  the  same  degree.  The  term  potential  is 
employed  in  this  connexion,  in  the  following  way :  —  A 
given  quantity  of  electricity  will  electrify  an  isolated  body 
up  to  a  certain  "  potential "  (or  power  of  doing  electric 
work)  depending  on  its  capacity.  A  large  quantity  of 
electricity  imparted  to  a  conductor  of  small  capacity  will 
electrify  it  up  to  a  very  high  potential;  just  as  a  large 
quantity  of  water  poured  into  a  vessel  of  narrow  capacity 
will  raise  the  surface  of  the  water  to  a  high  level  in  the 
vessel.  The  exact  definition  of  Potential,  in  terms  of 
energy  spent  against  the  electrical  forces,  is  given  in  the 
lesson  on  Electrostatics  (Art.  263). 

It  will  be  found  convenient  to  refer  to  a  positively 
electrified  body  as  one  electrified  to  a  positive  or  high 
potential;  while  a  negatively  electrified  body  may  be 
looked  upon  as  one  electrified  to  a  low  or  negative  poten- 
tial. And  just  as  we  take  the  level  of  the  sea  as  a  zero 
level,  and  measure  the  heights  of  mountains  above  it, 
and  the  depths  of  mines  below  it,  using  the  sea  level  as  a 
convenient  point  of  reference  for  differences  of  level,  so 
we  take  the  potential  of  the  earth's  surface  (for  the  sur- 
face of  the  earth  is  always  electrified  to  a  certain  degree) 
as  zero  potential,  and  use  it  as  a  convenient  point  of 
reference  from  which  to  measure  differences  of  electric 
potential. 


LESSON  V.  —  Electric  Machines 

41.  For  the  purpose  of  procuring  larger  supplies  of 
electricity  than  can  be  obtained  by  the  rubbing  of  a  rod 
of  glass  or  shellac,  electric  machines  have  been  devised. 
All  electric  machines  consist  of  two  parts,  one  for  pro- 
ducing, the  other  for  collecting,  the  electric  charges.  Ex- 
perience has  shown  that  the  quantities  of  +  and  —  elec- 


48  ELECTRICITY  AND   MAGNETISM        I-AUT  i 

trification  developed  by  friction  upon  the  two  surfaces 
rubbed  against  one  another  depend  on  the  amount  of 
friction,  upon  the  extent  of  the  surfaces  rubbed,  and  also 
upon  the  nature  of  the  substances  used.  If  the  two  sub- 
stances employed  are  near  together  on  the  list  of  electrics 
given  in  Art.  6,  the  electrical  effect  of  rubbing  them 
together  will  not  be  so  great  as  if  two  substances  widely 
separated  in  the  series  are  chosen.  To  obtain  the  highest 
effect,  the  most  positive  and  the  most  negative  of  the 
substances  convenient  for  the  construction  of  a  machine 
should  be  taken,  and  the  greatest  available  surface  of 
them  should  be  subjected  to  friction,  the  moving  parts 
having  a  sufficient  pressure  against  one  another  compati- 
ble with  the  required  velocity. 

The  earliest  form  of  electric  machine  was  devised  by 
Otto  von  Guericke  of  Magdeburg,  and  consisted  of  a 
globe  of  sulphur  fixed  upon  a  spindle,  and  pressed  with 
the  dry  surface  of  the  hands  while  being  made  to  rotate ; 
with  this  he  discovered  the  existence  of  electric  sparks 
and  the  repulsion  of  similarly  electrified  bodies.  Sir 
Isaac  Newton  replaced  Von  Guericke's  globe  of  sulphur 
by  a  globe  of  glass.  A  little  later  the  form  of  the 
machine  was  improved  by  various  German  electricians ; 
Von  Bose  added  a  collector  or  "  prime  conductor,"  in  the 
shape  of  an  iron  tube,  supported  by  a  person  standing  on 
cakes  of  resin  to  insulate  him,  or  suspended  by  silken 
strings ;  Winckler  of  Leipzig  substituted  a  leathern 
cushion  for  the  hand  as  a  rubber ;  and  Gordon  of  Erfurt 
rendered  the  machine  more  easy  of  construction  by  using 
a  glass  cylinder  instead  of  a  glass  globe.  The  electricity 
was  led  from  the  excited  cylinder  or  globe  to  the  prime 
conductor  by  a  metallic  chain  which  hung  over  against 
the  globe.  A  pointed  collector  was  not  employed  until 
after  Franklin's  famous  researches  on  the  action  of  points. 
About  1760  De  la  Fond,  Planta,  Ramsden,  and  Cuthbert- 
son,  constructed  machines  having  glass  plates  instead  of 
cylinders.  All  frictional  machines  are,  however,  now 


CHAP.    I 


FEICTIONAL   MACHINES 


obsolete,  having  in  recent  years  been  quite  superseded  by 
the  modern  Influence  Machines. 

42.  The  Cylinder  Electric  Machine.  — The  Cylinder 
Electric  Machine  consists  of  a  glass  cylinder  mounted 
on  a  horizontal  axis  capable  of  being  turned  by  a  handle. 
Against  it  is  pressed  from  behind  a  cushion  of  leather 
stuffed  with  horsehair,  the  surface  of  which  is  covered 
with  a  powdered  amalgam  of  zinc  or  tin.  A  flap  of  silk 
attached  to  the  cushion  passes  over  the  cylinder,  covering 
its  upper  half.  In  front  of  the  cylinder  stands  the 
"prime  conductor,"  which  is  made  of  metal,  and  usually 


Fig.  31. 

of  the  form  of  an  elongated  cylinder  with  hemispherical 
ends,  mounted  upon  a  glass  stand.  At  the  end  of  the 
prime  conductor  nearest  the  cylinder  is  fixed  a  rod  bear- 
ing a  row  of  fine  metallic  spikes,  resembling  in  form  a 
rake ;  the  other  end  usually  carries  a  rod  terminated  in 
a  brass  ball  or  knob.  The  general  aspect  of  the  machine 
is  shown  in  Fig.  31.  When  the  handle  is  turned  the 
friction  between  the  glass  and  the  amalgam-coated  sur- 
face of  the  rubber  produces  a  copious  electrical  action, 
electricity  appearing  as  a  +  charge  on  the  glass,  leaving 
the  rubber  with  a  —  charge.  The  prime  conductor  col- 
E 


50 


ELECTRICITY   AND   MAGNETISM        PART  i 


lects  this  charge  by  the  following  process  :  —  The  -f  charge 
being  carried  round  on  the  glass  acts  inductively  on  the 
long  insulated  conductor,  repelling  a  +  charge  to  the  far 
end ;  leaving  the  nearer  end  —  ly  charged.  The  effect  of 
the  row  of  points  is  to  emit  a  —  ly  electrified  wind  (see 
Art.  47)  towards  the  attracting  +  charge  upon  the  glass, 
which  is  neutralized  thereby ;  the  glass  thus  arriving 
at  the  rubber  in  a  neutral  condition  ready  to  be  again 
excited.  This  action  of  the  points  is  sometimes  described, 
though  less  correctly,  by  saying  that  the  points  collect  the 
+  charge  from  the  glass.  If  it  is  desired  to  collect  also 
the  —  charge  of  the  rubber,  the  cushion  must  be  supported 
on  an  insulating  stem  and  provided  at  the  back  with  a 
metallic  knob.  It  is,  however,  more  usual  to  use  only 
the  -f  charge,  and  to  connect  the  rubber  by  a  chain  to 
"  earth,"  so  allowing  the  -  charge  to  be  neutralized. 

43.  The  Plate  Electric  Machine.  —  The  Plate  Machine, 
as  its  name  implies,  is  constructed  with  a  circular  plate 

of  glass  or  of  ebo- 
nite, and  is  usually 
provided  with  two 
pairs  of  rubbers 
formed  of  double 
cushions,  pressing 
the  plate  between 
them,  placed  at  its 
highest  and  lowest 
point,  and  provided 
with  silk  flaps,  each 
i  extending  over  a 
quadrant  of  the 
circle.  The  prime 
conductor  is  either 
double  or  curved 
round  to  meet  the 
plate  at  the  two  ends  of  its  horizontal  diameter,  and  is 
furnished  with  two  sets  of  spikes,  for  the  same  purpose 


CHAP,  i     USE   OF  FRICTIONAL   MACHINES  51 

as  the  row  of  points  in  the  cylinder  machine.  A  common 
form  of  plate  machine  is  shown  in  Fig.  32.  The  action 
of  the  machine  is,  in  all  points  of  theoretical  interest,  the 
same  as  that  of  the  cylinder  machine.  Its  advantages 
are  that  a  large  glass  plate  is  more  easy  to  construct  than 
a  large  glass  cylinder  of  perfect  form,  and  that  the  length 
along  the  surface  of  the  glass  between  the  collecting  row 
of  points  and  the  edge  of  the  rubber  cushions  is  greater 
in  the  plate  than  in  the  cylinder  for  the  same  amount  of 
surface  exposed  to  friction ;  for,  be  it  remarked,  when  the 
two  charges  thus  separated  have  collected  to  a  certain 
extent,  a  discharge  will  take  place  along  this  surface,  the 
length  of  which  limits  therefore  the  power  of  the  machine. 
In  a  more  modern  form,  due  to  Le  Roy,  and  modified  by 
Winter,  there  is  but  one  rubber  and  flap,  occupying  a 
little  over  a  quadrant  of  the  plate,  and  one  collector  or 
double  row  of  points,  while  the  prime  conductor  consists 
of  a  ring-shaped  body. 

44.  Electric  Amalgam.  —  Canton,  finding  glass  to  be 
highly  electrified  when   dipped   into  dry  mercury,  sug- 
gested the  employment  of  an  amalgam  of  tin  with  mercury 
as  a  suitable  substance  wherewith  to  cover  the  surface  of 
the  rubbers.     Still  better  is  Kienmayer's  amalgam,  con- 
sisting of  equal  parts  of  tin  and  zinc,  mixed  while  molten 
with  twice  their  weight  of  mercury.     Bisulphide  of  tin 
("mosaic  gold")  may  also  be  used.     These  amalgams  are 
applied  to  the  cushions  with  a  little  stiff  grease.     They 
serve  the  double  purpose  of  conducting  away  the  negative 
charge  separated  upon  the  rubber  during  the  action  of 
the  machine,  and  of  affording  as  a  rubber  a  substance 
which  is  more  powerfully  negative  (see  list  in  Art.  6)  than 
the  leather  or  the  silk  of  the  cushion  itself.     Powdered 
graphite  is  also  good. 

45.  Precautions  in  using  Frictional  Machines.  —  Sev- 
eral precautions  must   be   observed   in  the  use  of  elec- 
trical machines.     Damp  and  dust  must  be  scrupulously 
avoided.     The  surface  of  glass   is   hygroscopic,   hence, 


52  ELECTRICITY   AND   MAGNETISM       PAKT  i 

except  in  the  driest  climates,  it  is  necessary  to  warm 
the  glass  surfaces  and  rubbers  to  dissipate  the  film  of 
moisture  which  collects.  Glass  sterns  for  insulation  may 
be  varnished  with  a  thin  coat  of  shellac  varnish,  or 
with  paraffin  (solid).  A  few  drops  of  anhydrous  paraffin 
(obtained  by  dropping  a  lump  of  sodium  into  a  bottle  of 
paraffin  oil),  applied  with  a  bit  of  flannel  to  the  pre- 
viously warmed  surfaces,  hinders  the  deposit  of  moist- 
ure. A  frictional  machine  which  has  not  been  used  for 
some  months  will  require  a  fresh  coat  of  amalgam  on  its 
rubbers.  These  should  be  cleaned  and  warmed,  a  thin 
uniform  layer  of  tallow  or  other  stiff  grease  is  spread 
upon  them,  and  the  amalgam,  previously  reduced  to  a  fine 
powder,  is  sifted  over  the  surface.  In  spite  of  all  pre- 
cautions friction  machines  are  uncertain  in  their  be- 
haviour in  damp  weather.  This  is  the  main  reason  why 
they  have  been  superseded  by  influence  machines,  which 
do  not  need  to  be  warmed. 

All  points  should  be  avoided  in  apparatus  for  frictional 
electricity  except  where  they  are  desired,  like  the  "  col- 
lecting "  spikes  on  the  prime  conductor,  to  let  off  a  charge 
of  electricity.  All  the  rods,  etc.,  in  frictional  apparatus 
are  therefore  made  with  rounded  knobs. 

46.  Experiments  with  the  Electric  Machine.  —  With 
the  electric  machine  many  pleasing  and  instructive  ex- 
periments are  possible.  The  phenomena  of  attraction  and 
repulsion  can  be  shown  upon  a  large  scale.  Fig.  33  repre- 
sents a  device  known  as  the  electric  chimes,*  in  which 
two  small  brass  balls  hung  by  silk  strings  are  set  in 
motion  and  strike  against  the  bells  between  which  they 
are  hung.  The  two  outer  bells  are  hung  by  metallic 
wires  or  chains  to  the  knob  of  the  machine.  The  third 
bell  is  hung  by  a  silk  thread,  but  communicates  with  the 
ground  by  a  brass  chain.  The  balls  are  first  attracted  to 

*  Invented  in  1752  by  Franklin,  for  the  purpose  of  warning  him  of  the 
presence  of  atmospheric  electricity,  drawn  from  the  air  above  his  house  by 
a  pointed  iron  rod. 


CHAP,  i    EXPERIMENTS    WITH   MACHINES 


53 


the  electrified  outer  bells,  then  repelled,  and,  having  dis- 
charged themselves  against  the  uninsulated  central  bell, 
are  again  attracted,  and  so  vibrate  to  and  fro. 

By  another  arrangement  small  figures  or  dolls  cut  out 
of  pith  can  be  made  to  dance  up  and  down  between  a 
metal  plate  hung  horizontally 
from  the  knob  of  the  machine, 
and  another  flat  plate  an  inch  ^ 
or  two  lower  and  communi- 
cating with  "earth." 

Another  favourite  way  of 
exhibiting  electric  repulsion 
is  by  means  of  a  doll  with 
long  hair  placed  on  the  ma- 
chine ;  the  individual  hairs 
stand  on  end  when  the  ma- 
chine is  worked,  being  re- 
pelled from  the  head,  and 
from  one  another.  A  paper 
tassel  will  behave  similarly 
if  hung  to  the  prime  con- 
ductor. The  most  striking  way  of  showing  this  pheno- 
menon is  to  place  a  person  upon  a  glass-legged  stool, 
making  him  touch  the  knob  of  the  machine  ;  when  the 
machine  is  worked,  his  hair,  if  dry,  will  stand  on  end. 
Sparks  will  pass  freely  between  a  person  thus  electrified 
and  one  standing  upon  the  ground. 

The  sparks  from  the  machine  may  be  made  to  kindle 
spirits  of  wine  or  ether,  placed  in  a  metallic  spoon,  con- 
nected by  a  wire,  with  the  nearest  metallic  conductor 
that  runs  into  the  ground.  A  gas  jet  may  be  lit  by 
passing  a  spark  to  the  burner  from  the  finger  of  the 
person  standing,  as  just  described,  upon  an  insulating 
stool. 

47.  Effect  of  Points  ;  Electric  Wind.  —  The  effect  of 
points  in  discharging  electricity  from  the  surface  of  a  con- 
ductor may  be  readily  proved  by  numerous  experiments. 


Fig.  38. 


54  ELECTRICITY   AND   MAGNETISM        PART  i 

If  the  machine  be  in  good  working  order,  and  capable  of 
giving,  say,  sparks  4  inches  long  when  the  knuckle  is 
presented  to  the  knob,  it  will  be  found  that,  on  fastening 
a  fine  pointed  needle  to  the  conductor,  it  discharges  the 
electricity  so  effectually  at  its  point  that  only  the  shortest 
sparks  can  be  drawn  at  the  knob,  while  a  fine  jet  or  brush 
of  pale  blue  light  will  appear  at  the  point.  If  a  lighted 
taper  be  held  in  front  of  the  point,  the  flame  will  be 
visibly  blown  aside  (Fig.  34)  by  the  streams  of  electrified 
air  repelled  from  the  point.  These  air-currents  can  be 


Fig.  34. 

felt  with  the  hand.  They  are  due  to  a  mutual  repulsion 
between  the  electrified  air  particles  near  the  point  and 
the  electricity  collected  on  the  point  itself.  That  this 
mutual  reaction  exists  is  proved  by  the  electric  fly  or 
electric  reaction-mill  of  Hamilton  (Fig.  35),  which  con- 
sists of  a  light  cross  of  brass  or  straw,  suspended  on  a 
pivot,  and  having  the  pointed  ends  bent  round  at  right 
angles.  When  placed  on  the  prime  conductor  of  the 
machine,  or  joined  to  it  by  a  chain,  the  force  of  repulsion 
between  the  electricity  of  the  points  and  that  on  the  air 


CHAP,  i     ELECTRIC    WINDS   FROM   POINTS 


55 


immediately  in  front  of  them  drives  the  mill  round  in 
the  direction  opposite  to  that  in  which  the  points  are 
bent.  It  will  even  rotate  if  immersed  in  turpentine  or 
petroleum.  If  the  points  of  the 
fly  are  covered  with  small  round 
lumps  of  wax  it  will  not  rotate, 
as  the  presence  of  the  wax  pre- 
vents the  formation  of  any 
wind  or  stream  of  electrified 
particles. 

The  electric  wind  from  a 
point  will  produce  a  charge 
upon  the  surface  of  any  insulat- 
ing body,  such  as  a  plate  of 
ebonite  or  glass,  held  a  few 
inches  away.  The  charge  may 
be  examined  by  dusting  red 
lead  or  lycopodium  powder 
upon  the  surface.  If  a  slip  of 
glass  or  mica  be  interposed  between  the  point  and  the 
surface  against  which  the  wind  is  directed,  an  electric 
shadow  will  be  formed  on  the  surface  at  the  part  so 
screened. 

48.  Armstrong's     Hydro-Electrical    Machine.  —  The 
friction  of  a  jet  of  steam  issuing  from  a  boiler,  through 
a  wooden  nozzle,  generates  electricity.     In  reality  it  is 
the  particles   of  condensed  water  in  the  jet  which  are 
directly  concerned.     Sir  W.  Armstrong,  who  investigated 
this  source  of  electricity,  constructed  a  powerful  appara- 
tus, known  as  the   hydro-electrical   machine,    capable  of 
producing  enormous  quantities  of  electricity,  and  yield- 
ing sparks  5  or  6  feet   long.     The  collector  consisted  of 
a  row  of  spikes,  placed  in   the  path  of  the   steam  jets 
issuing  from  wooden  nozzles,  and  was  supported,  together 
with  a  brass  ball  which  served  as  prime  conductor,  upon 
a  glass  pillar. 

49.  Influence  Machines.  —  There  is  another  class  of 


Fig.  35. 


56  ELECTRICITY    AND   MAGNETISM        PART  i 

electrical  machine,  differing  entirely  from  those  we  have 
been  describing,  and  depending  upon  the  principle  of 
influence.  They  also  have  been  termed  convection-induc- 
tion machines,  because  they  depend  upon  the  employment 
of  a  minute  initial  charge  which,  acting  by  influence, 
induces  other  charges,  which  are  then  conveyed  by  the 
moving  parts  of  the  machine  to  some  other  part,  where 
they  can  be  used  either  to  increase  the  initial  charge  or  to 
furnish  a  supply  of  electrification  to  a  suitable  collector. 
Of  such  instruments  the  oldest  is  the  Electrophone,  ex- 
plained fully  in  Lesson  III.  Bennet,  Nicholson,  Erasmus 
Darwin,  and  others  devised  pieces  of  apparatus  for  ac- 
complishing by  mechanism  that  which  the  electrophorus 
accomplishes  by  hand.  Nicholson's  revolving  doublet-,  in- 
vented in  1788,  consists  of  a  revolving  apparatus,  in  which 
an  insulated  carrier  can  be  brought  into  the  presence  of  an 
electrified  body,  there  touched  for  an  instant  while  under 
influence,  then  carried  forward  with  its  acquired  charge 
towards  another  body,  to  which  it  imparts  its  charge,  and 
which  in  turn  acts  inductively  on  it,  giving  it  an  opposite 
charge,  which  it  can  convey  to  the  first  body,  thus 
increasing  its  initial  charge  at  every  rotation. 

In  the  modern  influence  machines  two  principles  are 
embodied :  (1)  the  principle  of  influence,  namely,  that  a 
conductor  touched  while  under  influence  acquires  a  charge 
of  the  opposite  kind ;  (2)  the  principle  of  reciprocal  accu- 
mulation. This  principle  must  be  carefully  noted.  Let 
there  be  two  insulated  conductors  A  and  B  electrified  ever 
so  little,  one  positively,  the  other  negatively.  Let  a  third 
insulated  conductor  C,  which  will  be  called  a  carrier,  be 
arranged  to  move  so  that  it  first  approaches  A  and  then 
B,  and  so  forth.  If  touched  while  under  the  influence 
of  the  small  positive  charge  on  A  it  will  acquire  a  small 
negative  charge ;  suppose  that  it  then  moves  on  and 
gives  this  negative  charge  to  B.  Then  let  it  be  touched 
while  under  the  influence  of  B,  so  acquiring  a  small 
positive  charge.  When  it  returns  towards  A  let  it  give 


CHAP,  i  INFLUENCE   MACHINES  57 

up  this  positive  charge  to  A,  thereby  increasing  its 
positive  charge.  Then  A  will  act  more  powerfully,  and 
on  repeating  the  former  operations  both  B  and  A  will 
become  more  highly  charged.  Each  accumulates  the 
charges  derived  by  influence  from  the  other.  This  is  the 
fundamental  action  of  the  machines  in  question.  The 
modern  influence  machines  date  from  1860,  when  C.  F. 
Varley  produced  a  form  with  six  carriers  mounted  on  a 
rotating  disk  of  glass.  This  was  followed  in  1865  by 


Fig.  36. 

the  machine  of  Holtz  and  that  of  Toepler,  and  in  1867 
by  those  of  Lord  Kelvin  (the  "  replenisher "  and  the 
'"mouse-mill").  The  latest  forms  are  those  of  Mr. 
James  Wimshurst. 

50.  Typical  Construction.  —  Before  describing  some 
special  forms  we  will  deal  with  a  generalized  type  of 
machine  having  two  fixed  field-plates,  A  and  B,  which 
are  to  become  respectively  +  and  — ,  and  a  set  of  carriers, 
attached  to  a  rotating  disk  or  armature.  Fig.  36  gives  in 


58  ELECTRICITY   AND    MAGNETISM       PART  i 

a  diagrammatic  way  a  view  of  the  essential  parts.  For 
convenience  of  drawing  it  is  shown  as  if  the  metal  field- 
plates  A  and  B  were  affixed  to  the  outside  of  an  outer 
stationary  cylinder  of  glass ;  the  six  carriers  />,  q,  r,  s,  t, 
and  u  being  attached  to  the  inside  of  an  inner  rotating 
cylinder.  The  essential  parts  then  are  as  follows :  — 

(i.)    A  pair  of  field-plates  A  and  B. 

(ii.)    A  set  of  rotating  carriers  p,  q,  r,  s,  t,  and  u. 

(iii.)  A  pair  of  neutralizing  brushes  nv  n2  made  of 
flexible  metal  wires,  the  function  of  which  is 
to  touch  the  carriers  while  they  are  under  the 
influence  of  the  field-plates.  They  are  con- 
nected together  by  a  diagonal  conductor,  which 
need  not  be  insulated. 

(iv.)  A  pair  of  appropriating  brushes  av  «2,  which  reach 
over  from  the  field-plates  to  appropriate  the 
charges  that  are  conveyed  around  by  the 
carriers,  and  impart  them  to  the  field-plates. 

(v.)  In  addition  to  the  above,  which  are  sufficient  to 
constitute  a  complete  self-exciting  machine,  it 
is  usual  to  add  a  discharging  apparatus,  con- 
sisting of  two  combs  cv  c2,  to  collect  any  unap- 
propriated charges  from  the  carriers  after  they 
have  passed  the  appropriating  brushes ;  these 
combs  being  connected  to  the  adjustable  dis- 
charging balls  at  D. 

The  operation  of  the  machine  is  as  follows.  The 
neutralizing  brushes  are  set  so  as  to  touch  the  moving1 
carriers  just  before  they  pass  out  of  the  influence  of  the 
field-plates.  Suppose  the  field-plate  A  to  be  charged  ever 
so  little  positively,  then  the  carrier  />,  touched  by  nl  just 
as  it  passes,  will  acquire  a  slight  negative  charge,  which 
it  will  convey  forward  to  the  appropriating  brush  ar  and 
will  thus  make  B  slightly  negative.  Each  of  the  carriers 
as  it  passes  to  the  right  over  the  top  will  do  the  same 
thing.  Similarly  each  of  the  carriers  as  it  passes  from 


CHAP,  i  INFLUENCE  MACHINES  59 

right  to  left  at  the  lower  side  will  be  touched  by  n2  while 
under  the  influence  of  the  --  charge  on  B,  and  will 
convey  a  small  +  charge  to  A  through  the  appropriating 
brush  «2.  In  this  way  A  will  rapidly  become  more  and 
more  +,  and  B  more  and  more  —  ;  and  the  more  highly 
charged  they  become,  the  more  do  the  collecting  combs 
cl  and  c2  receive  of  unappropriated  charges.  Sparks  will 
snap  across  between  the  discharging  knobs  at  D. 

The  machine  will  not  be  self-exciting  unless  there  is  a 
good  metallic  contact  made  by  the  neutralizing  brushes  and 
by  the  appropriating  brushes.  If  the  discharging  apparatus 
were  fitted  at  cv  c.2  with  contact  brushes  instead  of  spiked 
combs,  the  machine  would  be  liable  to  lose  the  charge  of 
the  field-plates,  or  even  to  have  their  charges  reversed  in 
sign  whenever  a  large  spark  was  taken  from  the  knobs. 

It  will  be  noticed  that  there  are  two  thicknesses  of 
glass  between  the  fixed  field-plates  and  the  rotating  carriers. 
The  glass  serves  not  only  to  hold  the  metal  parts,  but 
prevents  the  possibility  of  back-discharges  (by  sparks  or 
winds)  from  the  carriers  to  the  field-plates  as  they  pass. 

The  essential  features  thus  set  forth  will  be  found  in 
Varley's  machine  of  1860,  in  Lord  Kelvin's  "replenisher" 
(which  had  only  two  carriers),  and  in  many  other  machines 
including  the  apparatus  known  as  Clarke's  "gas-lighter." 

51.  Toepler's  Influence  Machine.  —  In  this  machine, 
as  constructed  by  Voss,  are  embodied  various  points  due 
to  Holtz  and  others.  Its  construction  follows  almost 
literally  the  diagram  already  explained,  but  instead  of 
having  two  cylinders,  one  inside  the  other,  it  has  two 
flat  disks  of  varnished  glass,  one  fixed,  the  other  slightly 
smaller  rotating  in  front  of  it  (Fig.  37).  The  field-plates 
A  and  B  consist  of  pieces  of  tinfoil,  cemented  on  the 
back  of  the  back  disk,  each  protected  by  a  coating  of 
varnished  paper.  The  carriers  are  small  disks  or  sectors 
of  tinfoil,  to  the  number  of  six  or  eight,  cemented  to  the 
front  of  the  front  disk.  To  prevent  them  from  being 
worn  away  by  rubbing  against  the  brushes  a  small 


60 


ELECTRICITY  AND   MAGNETISM       PART  i 


metallic  button  is  attached  to  the  middle  of  each.  The 
neutralizing  brushes  nv  n2  are  small  whisps  of  fine 
springy  brass  wire,  and  are  mounted  on  the  ends  of  a 
diagonal  conductor  Z.  The  appropriating  brushes  av  a2 
are  also  of  thin  brass  wire,  and  are  fastened  to  clamps 
projecting  from  the  edge  of  the  fixed  disk,  so  that  they 
communicate  metallically  with  the  two  field-plates.  The 
collecting  combs,  which  have  brass  spikes  so  short  as  not 
to  touch  the  carriers,  are  mounted  on  insulating  pillars 
and  are  connected  to  the  adjustable  discharging  knobs 


FRONT  ROTATING   DISK 
WITH  CARRIERS  ON  FRONT. 


Fig.  37. 


Dj,  D2.  These  also  communicate  with  two  small  Leyden 
jars  J1?  J2,  the  function  of  which  is  to  accumulate  the 
charges  before  any  discharge  takes  place.  These  jars  are 
separately  depicted  in  Fig.  38.  Without  them,  the  dis- 
charges between  the  knobs  take  place  in  frequent  thin 
blue  sparks.  With  them  the  sparks  are  less  numerous, 
but  very  brilliant  and  noisy. 

To  use  the  Toepler  (Voss)  machine  first  see  that  all 
the  four  brushes  are  so  set  as  to  make  good  metallic  con- 
tact with  the  carriers  as  they  move  past,  and  that  the 


CHAP,  i    TOEPLER  (VOSS)  INFLUENCE  MACHINE    61 

neutralizing  brushes  are  set  so  as  to  touch  the  carriers 
while  under  influence.  Then  see  that  the  discharging 
knobs  are  drawn  widely  apart.  Set  the  machine  in 
rotation  briskly.  If  it  is  clean  it  should  excite  itself 
after  a  couple  of  turns,  and  will  emit  a  gentle  hissing- 
sound,  due  to  internal  discharges  (visible  as  blue  glimmers 
in  the  dark),  and  will  offer  more  resistance  to  turning. 
If  then  the  knobs  are  pushed  nearer  together  sparks  will 
pass  across  between  them.  The  jars  (the  addition  of 
which  we  owe  to  Holtz)  should  be  kept  free  from  dust. 
Sometimes  a  pair  of  terminal  screws  are  added  at  Sp  S2 
(Fig.  38),  connected  respectively  with  the  outer  coatings 


•  .1 


Fig.  33. 

of  the  jars.  These  are  convenient  for  attaching  wires  to 
lead  away  discharges  for  experiments  at  a  distance.  If 
not  so  used  they  should  be  joined  together  by  a  short 
wire,  as  the  two  jars  will  not  work  properly  unless  their 
outer  coatings  are  connected. 

52.  Wimshurst's  Influence  Machine.  —  In  this,  the 
most  widely  used  of  influence  machines,  there  are  no 
fixed  field-plates.  In  its  simplest  form  it  consists  (Fig. 
39)  of  two  circular  plates  of  varnished  glass,  which  are 
geared  to  rotate  in  opposite  directions.  A  number  of 
sectors  of  metal  foil  are  cemented  to  the  front  of  the 
front  plate  and  to  the  back  of  the  back  plate ;  these 
sectors  serve  both  as  carriers  and  as  inductors.  Across 


62 


ELECTRICITY   AND   MAGNETISM       PART 


the  front  is  fixed  an  uninsulated  diagonal  conductor, 
carrying  at  its  ends  neutralizing  brushes,  which  touch 
the  front  sectors  as  they  pass.  Across  the  back,  but 
sloping  the  other  way,  is  a  second  diagonal  conductor, 
with  brushes  that  touch  the  sectors  on  the  hinder  plate. 
Nothing  more  than  this  is  needed  for  the  machine  to 
excite  itself  when  set  in  rotation ;  but  for  convenience 


Fig.  39. 

there  is  added  a  collecting  and  discharging  apparatus. 
This  consists  of  two  pairs  of  insulated  combs,  each  pair 
having  its  spikes  turned  inwards  toward  the  revolving 
disks,  but  not  touching  them ;  one  pair  being  on  the 
right,  the  other  on  the  left,  mounted  each  on  an  insulat- 
ing pillar  of  ebonite.  These  collectors  are  furnished 
with  a  pair  of  adjustable  discharging  knobs  overhead; 


CHAP,  i     WIMSHURST   INFLUENCE   MACHINE 


63 


and  sometimes  a  pair  of  Leyden  jars  is  added,  to  prevent 
the  sparks  from  passing  until  considerable  quantities  of 
charge  have  been  collected. 

The  processes  that  occur  in  this  machine  are  best 
explained  by  aid  of  a  diagram  (Fig.  40),  in  which,  for 
greater  clearness,  the  two  rotating  plates  are  represented 


Fig.  40. 

as  though  they  were  two  cylinders  of  glass,  rotating 
opposite  ways,  one  inside  the  other.  The  inner  cylinder 
will  represent  the  front  plate,  the  outer  the  back  plate. 
In  Figs.  39  and  40  the  front  plate  rotates  right-handedly, 
the  back  plate  left-handedly.  The  neutralizing  brushes 
nr  n2  touch  the  front  sectors,  while  n3,  n4  touch  against 
the  back  sectors. 


64  ELECTRICITY   AND   MAGNETISM       PART  i 

Now  suppose  any  one  of  the  back  sectors  represented 
near  the  top  of  the  diagram  to  receive  a  slight  positive 
charge.     As  it  is  moved  onward  toward  the  left  it  will 
come  opposite  the  place  where  one  of  the  front  sectors  is 
moving  past  the  brush  nr     The  result  will  be  that  the 
sector  so  touched  while  under  influence  by  n^  will  acquire 
a  slight  negative  charge,  which  it  will  carry  onwards 
toward  the  right.      When  this  negatively-charged  front 
sector  arrives  at  a  point  opposite  n3  it  acts  inductively  on 
the  back  sector  which  is  being  touched  by  na;   hence 
this  back  sector  will  in  turn  acquire  a  positive  charge, 
which  it  will  carry  over  to  the  left.     In  this  way  all  the 
sectors  will  become  more  and  more  highly  charged,  the 
front  sectors  carrying  over  negative  charges  from  left  to 
right,  and  the  back  sectors  carrying  over  positive  charges 
from  right  to  left.     At  the  lower  half  of  the  diagram  a 
similar  but  inverse  set  of  operations  will  be  taking  place. 
For  when  n^  touches  a  front  sector  under  the  influence  of 
a  positive  back  sector,  a  repelled  charge  will  travel  alorfg 
the  diagonal  conductor  to  n2,  helping  to  charge  positively 
the  sector  which  it  touches.     The  front  sectors,  as  they 
pass  from  right  to  left  (in  the  lower  half),  will  carry 
positive  charges,  while  the  back  sectors,  after  touching 
n4,  will  carry  negative  charges  from  left  to  right.     The 
metal  sectors  then  act  both  as  carriers  and  as  inductors. 
It  is  clear  that  there  will  be  a  continual  carrying  of  posi- 
tive charges  toward  the  right,  and  of  negative  charges 
to  the  left.     At  these  points,  toward  which  the  opposite 
kinds  of  charges  travel,  are  placed  the  collecting-combs 
communicating  with  the  discharging  knobs.     The  latter 
ought  to  be  opened  wide  apart  when  starting  the  machine, 
and  moved  together  after  it  has  excited  itself. 

In  larger  Wimshurst  influence  machines  two,  three, 
or  more  pairs  of  oppositely-rotating  plates  are  mounted 
within  a  glass  case  to  keep  off  the  dust.  If  the  neutral- 
izing brushes  make  good  metallic  contact  these  machines 
are  all  self-exciting  in  all  weathers.  Machines  with  only 


CHAP,  i         HOLTZ   INFLUENCE   MACHINE  65 

six  or  eight  sectors  on  each  plate  give  longer  sparks,  but 
less  frequently  than  those  that  have  a  greater  number. 
Mr.  Wimshurst  has  designed  many  influence  machines, 
from  small  ones  with  disks  2  inches  across  up  to  that  at 
Sbuth  Kensington,  which  has  plates  7  feet  in  diameter. 

Prior  to  Wimshurst's  machine  Holtz  had  constructed 
one  with  two  oppositely-rotating  glass  disks;  but  they 
had  no  metal  carriers  upon  them.  It  was  not  self -exciting. 

53.  Holtz's  Influence  Machine.  —  The  Holtz  machine 
in  its  typical  form  had  the  following  peculiarities. 
There  were  no  metal  carriers  upon  the  rotating  plate, 
hence  another  mode  of  charging  it  had  to  be  adopted  in 
lieu  of  touching  conductors 
while  under  influence, 
as  will  be  seen.  The 
field-plates  A  and  B  (Fig. 
41)  were  of  varnished 
paper  —  a  poor  conductor 
—  fastened  upon  the  back 
of  the  fixed  disk.  In  the 
fixed  disk  of  glass,  on 
which  the  field-plates  were 
mounted,  there  were  cut 
two  windows  or  openings, 
through  which  there  pro- 
jected from  the  field-plates  two  pointed  paper  tongues, 
which  took  the  place  of  appropriating  brushes.  The 
discharging  knobs  were  inserted  in  the  neutralizing  cir- 
cuit which  united  two  metal  combs  with  pointed  spikes, 
situated  in  front  of  the  rotating  front  disk,  opposite  the 
two  field-plates.  There  was  (at  first)  no  diagonal  con- 
ductor. It  will  be  noted  that  while  the  combs,  which 
served  both  as  neutralizing  and  collecting  combs,  were  in 
front  of  the  rotating  plate,  the  appropriating  tongues 
were  situated  at  the  back  of  the  same.  Fig.  41  is  a 
view  of  the  machine  from  behind.  The  machine  was 
not  self-exciting.  In  operating  it  the  following  procedure 


66  ELECTRICITY   AND   MAGNETISM        PART  i 

was  used :  first  the  two  discharging  knobs  were  put 
together,  then  the  front  disk  was  set  into  rapid  rotation. 
While  so  rotating  a  small  initial  charge  was  communi- 
cated to  one  of  the  field-plates  by  holding  to  it  a  rubbed 
piece  of  ebonite  or  glass,  or  by  sending  into  it  a  spai«k 
from  a  Leyden  jar.  Thereupon  the  machine  charged 
itself,  and  began  to  emit  pale  blue  sparks  from  the  points 
of  the  combs  and  tongues  with  a  hissing  sound.  On  then 
drawing  apart  the  discharging  knobs,  a  torrent  of  sparks 
rushed  across. 

These  arrangements  being  known,  it  is  not  difficult 
to  follow  the  action  of  the  machine,  provided  it  is  once 
understood  that  the  whole  operation  depends  upon  the 
circumstance  that  the  surface  of  a  non-conducting  body 
such  as  glass  can  be  electrified  by  letting  off  against  it 
an  electric  wind  from  a  point  placed  near  it  (see  Art.  47). 
Suppose  that  a  small  initial  +  charge  is  given  to  A.  This 
will  operate  by  influence  upon  the  metal  parts  imme- 
diately opposite  it,  and  cause  the  spikes  to  become  elec- 
trified negatively,  and  to  give  off  a  negatively  electrified 
wind,  which  will  charge  the  face  of  the  rotating  plate, 
these  charges  being  then  carried  over  to  the  other  side, 
where  the  spikes  of  the  other  comb  will  be  emitting  a 
positively  electrified  wind.  The  pointed  tongues  which 
project  towards  the  back  of  the  rotating  disk  also  let  off: 
winds,  the  tendency  being  always  for  them  to  charge  the 
back  of  the  plate  with  a  charge  of  opposite  sign  from 
that  which  is  coming  toward  them  on  the  front.  If 
negative  charges  are  being  carried  over  the  top  on  the 
front,  then  the  tongue  of  B  will  tend  to  let  off  a  positive 
charge  against  the  back,  thereby  leaving  B  more  negative. 
In  the  same  way  the  tongue  of  A  will  let  off  a  negatively 
electrified  wind,  making  A  more  positive,  so  building  up 
or  accumulating  two  opposite  kinds  of  charges  on  the 
two  field-plates.  This  action  will  not  occur  unless  the 
moving  plate  rotates  in  the  direction  opposite  to  that  in 
which  the  two  tongues  point. 


CHAP,  i         HOLTZ   INFLUENCE   MACHINE  67 

The  defects  of  the  Holtz  machine  were  that  it  was  so 
sensitive  to  damp  weather  as  to  be  unreliable,  that  it  was 
apt  suddenly  to  reverse  its  charges,  and  that  the  electric 
winds  by  which  it  operated  could  not  be  produced  with- 
out a  sufficiently  great  initial  charge. 

In  later  Holtz  machines  a  number  of  rotating  disks 
fixed  upon  one  common  axis  were  employed,  the  whole 
being  enclosed  in  a  glass  case  to  prevent  the  access  of 
damp.  A  small  disk  of  ebonite  was  sometimes  fixed  to 
the  same  axis,  and  provided  with  a  rubber,  in  order  to 
keep  up  the  initial  charge  by  friction.  Holtz  constructed 
many  forms  of  machine,  including  one  with  thirty-two 
plates,  besides  machines  of  a  second  kind  having  two 
glass  plates  rotating  in  opposite  directions. 

The  Holtz  machine,  as  indeed  every  kind  of  influence 
machine,  is  reversible  in  its  action ;  that  is  to  say,  that  if 
a  continuous  supply  of  the  two  electricities  (furnished  by 
another  machine)  be  communicated  to  the  armatures,  the 
movable  plate  will  be  thereby  set  in  rotation  and,  if 
allowed  to  run  quite  freely,  will  turn  in  an  opposite  sense. 

Righi  showed  that  a  Holtz  machine  can  yield  a  con- 
tinuous current  like  a  voltaic  battery,  the  strength  of 
the  current  being  nearly  proportional  to  the  velocity  of 
rotation.  It  was  found  that  the  electromotive-force  of  a 
machine  was  equal  to  that  of  52,000  Daniell's  cells,  or 
nearly  53,000  volts,  at  all  speeds.  The  resistance  when 
the  machine  made  120  revolutions  per  minute  was  2810 
million  ohms ;  but  only  646  million  ohms  when  making 
450  revolutions  per  minute. 

54.  Experiments  with  Influence  Machines.  —  The 
experiments  described  in  Art.  43,  and  indeed  all  those 
usually  made  with  the  old  frictional  machines,  includ- 
ing the  charging  of  Leyden  jars,  can  be  performed 
by  the  aid  of  influence  machines.  In  some  cases  it  is 
well  to  connect  one  of  the  two  discharging  knobs  to  the 
earth  by  a  wire  or  chain,  and  to  take  the  discharge  from 
the  other  knob.  To  illuminate  small  vacuum  tubes  they 


68  ELECTRICITY  AND   MAGNETISM       PART  i 

may  be  connected  by  guttapercha-covered  wires  to  the 
two  discharging  knobs,  or  to  the  terminals  Sr  S2  of 
Fig.  38.  The  curious  property  of  the  electric  discharge 
from  a  point  in  collecting  dust  or  fumes  is  readily  shown 
by  connecting  by  a  wire  a  needle  which  is  introduced 
into  a  bell-jar  of  glass.  The  latter  is  filled  with  fumes 
by  burning  inside  it  a  bit  of  magnesium  wire,  or  of  brown 
paper.  Then  on  turning  the  handle  of  the  influence 
machine  the  fumes  are  at  once  deposited,  and  the  air  left 
clear. 


LESSON  VI.  —  The  Leyden  Jar  and  other  Condensers 

55.  It  was  shown  in  previous  lessons  that  the  opposite 
charges  of  electricity  attract  one  another;  that  electricity 
cannot  flow  through  glass ;  and  that  yet  electricity  can 
act  across  glass  by  influence.  Two  suspended  pith-balls,  one 
electrified  positively  and  the  other  negatively,  will  attract 
one  another  across  the  intervening  air.  If  a  plate  of  glass 
be  put  between  them  they  will  still  attract  one  another, 
though  neither  they  themselves  nor  the  electric  charges 
on  them  can  pass  through  the  glass.  If  a  pith-ball 
electrified  with  a  —  charge  be  hung  inside  a  dry  glass 
bottle,  and  a  rubbed  glass  rod  be  held  outside,  the  pith- 
ball  will  rush  to  the  side  of  the  bottle  nearest  to  the  glass 
rod,  being  attracted  by  the  +  charge  thus  brought  near  it. 
If  a  pane  of  glass  be  taken,  and  a  piece  of  tinfoil  be  stuck 
upon  the  middle  of  each  face  of  the  pane,  and  one  piece 
of  tinfoil  be  charged  positively,  and  the  other  negatively, 
the  two  charges  will  attract  one  another  across  the  glass, 
and  will  no  longer  be  found  to  be  free.  If  the  pane  is 
set  up  on  edge,  so  that  neither  piece  of  tinfoil  touches  the 
table,  it  will  be  found  that  hardly  any  electricity  can  be 
got  by  merely  touching  either  of  the  foils,  for  the  charges 
are  "  bound,"  so  to  speak,  by  each  other's  attractions  ; 
each  charge  is  inducing  the  other.  In  fact  it  will  be 


CHAP. 


CONDENSERS 


C9 


found  that  these  two  pieces  of  tinfoil  may  be,  in  this 
manner,  charged  a  great  deal  more  strongly  than  either  of 
them  could  possibly  be  if  it  were  stuck  to  a  piece  of  glass 
alone,  and  then  electrified.  In  other  words,  the  capacity 
of  a  conductor  is  greatly  increased  when  it  is  placed  near  to  a 
conductor  electrified  with  the  opposite  kind  of  charge.  If  its 
capacity  is  increased,  a  greater  quantity  of  electricity  may 
be  put  into  it  before  it  is  charged  to  an  equal  degree  of 
potential.  Hence,  such  an  arrangement  for  holding  a 
large  quantity  of  electrification  may  be  called  a  condenser 
of  electricity. 

56.   Condensers.  —  Next,  suppose  that  we  have  two 
brass  disks,  A  and  B  (Fig.  42),  set  upon  insulating  stems, 
and  that  a  glass  plate  is  placed  between  them.     Let  B  be 
connected  by  a  wire 
to   the  knob  of  an 
electrical     machine, 
and  let  A  be  joined 
by  a  wire  to  "earth." 
The  +  charge  upon 
B    will    act    induc- 
tively    across      the 
glass    plate    on    A, 
and  will  repel  elec-  Fig.  42. 

tricity  into  the  earth, 

leaving  the  nearest  face  of  A  negatively  electrified.  This 
—  charge  on  A  will  attract  the  +  charge  of  B  to  the  side 
nearest  the  glass,  and  a  fresh  supply  of  electricity  will  come 
from  the  machine.  Thus  this  arrangement  will  become  a 
condenser.  If  the  two  brass  disks  are  pushed  up  close  to 
the  glass  plate  there  will  be  a  still  stronger  attraction 
between  the  +  and  —  charges,  because  they  are  now  nearer 
one  another,  and  the  inductive  action  will  be  greater ;  hence 
a  still  larger  quantity  can  be  accumulated  in  the  plates. 
We  see  then  that  the  capacity  of  a  condenser  is  increased 
by  bringing  the  plates  near  together.  If  now,  while  the 
disks  are  strongly  charged,  the  wires  are  removed  and  the 


70  ELECTRICITY   AND   MAGNETISM        PART  i 

disks  are  drawn  backwards  from  one  another,  the  two 
charges  will  not  hold  one  another  bound  so  strongly,  and 
there  will  be  more  free  electrification  than  before  over  their 
surfaces.  This  would  be  rendered  evident  to  the  experi- 
menter by  the  little  pith-ball  electroscopes  fixed  to  them 
(see  the  Fig.),  which  would  fly  out  as  the  brass  disks  were 
moved  apart.  We  have  put  no  further  charge  on  the 
disk  B,  and  yet,  from  the  indications  of  the  electroscope, 
we  should  conclude  that  by  moving  it  away  from  disk  A 
it  has  become  electrified  to  a  higher  degree.  The  fact  is, 
that  while  the  conductor  B  was  near  the  —  charge  of  A 
the  capacity  of  B  was  greatly  increased,  but  on  moving  it 
away  from  A  its  capacity  has  diminished,  and  hence  the 
same  quantity  of  electricity  now  electrifies  it  to  a  higher 
degree  than  before.  The  presence,  therefore,  of  an  earth- 
connected  plate  near  an  insulated  conductor  increases  its 
capacity,  and  permits  it  to  accumulate  a  greater  charge 
by  attracting  and  condensing  the  electricity  upon  the  face 
nearest  the  earth-plate,  the  surface-density  on  this  face 
being  therefore  very  great ;  hence  the  appropriateness  of 
the  term  condenser  as  applied  to  the  arrangement.  It  was 
formerly  also  called  an  accumulator ;  but  the  term  accu- 
mulator is  now  reserved  for  the  special  kind  of  battery  for 
storing  the  energy  of  electric  currents  (Art.  492). 

The  stratum  of  air  between  the  two  disks  will  suffice 
to  insulate  the  two  charges  one  from  the  other.  The 
brass  disks  thus  separated  by  a  stratum  of  air  constitute 
an  air-condenser,  or  air-leyden.  Such  condensers  were 
first  devised  by  Wilcke  and  Aepinus.  In  these  experi- 
ments the  sheet  of  glass  or  layer  of  air  acts  as  a  dielectric 
(Art.  295)  conveying  the  inductive  action  through  its 
substance.  All  dielectrics  are  insulators,  but  equally 
good  insulators  are  not  necessarily  equally  good  dielec- 
trics. Air  and  glass  are  far  better  insulators  than  ebonite 
or  paraffin  in  the  sense  of  being  much  worse  conductors. 
But  influence  acts  more  strongly  across  a  slab  of  glass 
than  across  a  slab  of  ebonite  or  paraffin  of  equal  thickness, 


CHAP,  i  DISPLACEMENT  71 

and  better  still  across  these  than  across  a  layer  of  air.  In 
other  words,  glass  is  a  better  dielectric  than  ebonite,  or 
paraffin,  or  air,  as  it  possesses  a  higher  inductive  capacity. 
It  will  then  be  seen  that  in  the  act  of  charging  a  con- 
denser, as  much  electricity  flows  out  at  one  side  as  flows 
in  at  the  other. 

57.  Displacement.  —  Whenever  electric  forces  act  on 
a  dielectric,  tending  to  drive  electricity  in  at  one  side  and 
out  at  the  other,  we  may  draw  lines  of  force  through  the 
dielectric  in  the  direction  of  the  action,  and  we  may  con- 
sider tubular  spaces  mapped  out  by  such  lines.     We  may 
consider  a  tube  of  electric  force  having   at  one  end  a 
definite  area  of  the  positively  charged  surface,  and  at  the 
other  end  an  area  of   the   negatively  charged   surface. 
These  areas  may  be  of  different  size  or  shape,  but  the 
quantities   of  +  and  —  electrification  over  them  will  be 
equal.     The  quantity  of  electricity  which  has  apparently 
been  transferred  along  the  tube  was  called  by  Maxwell 
"  the  displacement"     In  non-conductors  it  is  proportional 
to  the  electromotive-force.     In  conductors  electromotive 
forces  produce  currents,  which  may  be  regarded  as  dis- 
placements which  increase  continuously  with  time.     In 
certain  crystalline  media  the  displacement  does  not  take 
place  exactly  in  the  direction  of  the  electric  force  :   in 
this  case  we  should  speak  of  tubes  of  influence  rather 
than  tubes  of  force.     A  unit  tube  will  be  bounded  at  its 
two  ends  by  unit  charges  -f  and  — .      We  may  consider 
the  whole  electric  field  between  positively  and  negatively 
charged  bodies  as  mapped  out  into  such  tubes. 

58.  Capacity  of  a  Condenser.  —  It  appears,  therefore, 
that  the  capacity  of  a  condenser  will  depend  upon  — 

(1)  The  size  and  form  of  the  metal  plates  or  coatings. 

(2)  The  thinness  of  the  stratum  of  dielectric  between 

them ;  and 

(3)  The  dielectric  capacity  of  the  material. 

59.  The  Leyden  Jar.  —  The  Ley  den  jar,  called  after 
the  city  where  it  was  invented,  is  a  convenient  form  of 


72  ELECTKICITY   AND   MAGNETISM        PART  i 

condenser.  It  usually  consists  (Fig.  43)  of  a  glass  jar 
coated  up  to  a  certain  height  on  the  inside  and  outside 
with  tinfoil.  A  brass  knob  fixed  on  the  end  of  a  stout 
brass  wire  passes  downward  through  a  lid  or  top  of  dry 
well-varnished  wood,  and  communicates  by  a  loose  bit  of 
brass  chain  with  the  inner  coating  of  foil.  To  charge  the 
jar  the  knob  is  held  to  the  prime  conductor  of  an  electrical 
machine,  the  outer  coating 
being  either  held  in  the  hand 
or  connected  to  "  earth  "  by  a 
wire  or  chain.  When  a  -f 
charge  of  electricity  is  im- 
parted thus  to  the  inner  coat- 
ing, it  acts  inductively  on  the 
outer  coating,  attracting  a  — 
charge  into  the  face  of  the 
outer  coating  nearest  the  glass, 
and  repelling  a  +  charge  to  the 
outside  of  the  outer  coating, 

and  thence  through  the  hand  or  wire  to  earth.  After 
a  few  moments  the  jar  will  have  acquired  its  full 
charge,  the  outer  coating  being  —  and  the  inner +.  If 
the  jar  is  of  good  glass,  and  dry,  and  free  from  dust,  it 
will  retain  its  charge  for  many  hours  or  days.  But  if  a 
path  be  provided  by  which  the  two  mutually  attracting 
electricities  can  flow  to  one  another,  they  will  do  so,  and 
the  jar  will  be  instantaneously  discharged.  If  the  outer 
coating  be  grasped  with  one  hand,  and  the  knuckle  of  the 
other  hand  be  presented  to  the  knob  of  the  jar,  a  bright 
spark  will  pass  between  the  knob  and  the  knuckle  with 
a  sharp  report,  and  at  the  same  moment  a  convulsive 
"  shock "  will  be  communicated  to  the  muscles  of  the 
wrists,  elbows,  and  shoulders.  A  safer  means  of  dis- 
charging the  jar  is  afforded  by  the  discharging  tongs 
or  discharger  (Fig.  44),  which  consists  of  a  jointed  brass 
rod  provided  with  brass  knobs  and  a  glass  handle.  One 
knob  is  laid  against  the  outer  coating,  the  other  is  then 


CHAP,  i  LEYDEN  JAR  73 

brought  near  the  knob  of  the  jar,  and  a  bright  snapping 

spark  leaping  from  knob  to  knob  announces  that  the  two 

accumulated    charges     have     flowed 

together,   completing    the   discharge. 

Sometimes  a  jar  discharges  itself  by 

a  spark  climbing  over  the  top  edge  of 

the  jar.      Often  when   a  jar  is  well 

charged  a  hissing  sound  is  heard,  due 

to  partial    discharges   creeping  over 

the  edge.     They  can  be  seen  in  the 

dark  as  pale  phosphorescent  streams. 

60.  Discovery  of  the  Ley  den  Jar. 
—  The  discovery  of   the    Leyden  jar 
arose  from  the  attempt  of  Musschen- 
broek  and  his  pupil  Cuneus  *  to  col- 
lect the  supposed  electric  "  fluid  "  in  a  bottle  half  filled 
with  water,  which  was  held  in  the  hand  and  was  provided 
with  a  nail  to  lead  the  "  fluid  "  down  through  the  cork 
to  the  water  from  the  electric  machine.     Here  the  water 
served  as   an   inner  coating    and   the  hand  as  an  outer 
coating  to  the  jar.     Cuneus  on  touching  the  nail  received 
a  shock.     This  accidental  discovery  created  the  greatest 
excitement  in  Europe  and  America. 

61.  Residual  Charges. —  If  a  Leyden  jar  be  charged 
and  discharged  and  then  left  for  a  little  time  to  itself, 
it   will   be   found    on   again   discharging    that    a   small 
second    spark    can    be    obtained.     There    is    in    fact   a 
residual   charge  which   seems   to   have   soaked   into   the 
glass   or  been   absorbed.     The    return    of   the   residual 
charge  is  hastened  by  tapping  the  jar.     The  amount  of 
the  residual  charge  varies  with  the  time  that  the  jar  has 
been  left  charged;   it  also  depends  on  the  kind  of  the 
glass  of  which  the  jar  is  made.     There  is  no  residual 
charge  discoverable  in  an  air-leyden   after  it  has  once 
been  discharged. 

*  The  honour  of  the  invention  of  the  jar  is  also  claimed  for  Kleist, 
Bishop  of  Pomerania. 


74 


ELECTRICITY   AND    MAGNETISM        PART 


62.  Batteries  of  Leyden  Jars.  —  A  large  Leyden  jar 
will  give  a  more  powerful  shock  than  a  small  one,  for  a 
larger  charge  can  be  put  into  it ;  its  capacity  is  greater. 
A  Leyden  jar  made  of  thin  glass  has  a  greater  capacity 
as  a  condenser  than  a  thick  one  of  the  same  size ;  but  if 
it  is  too  thin  it  will  be  destroyed  when  powerfully  charged 


Fig.  45. 

by  a  spark  actually  piercing  the  glass.  "Toughened" 
glass  is  less  easily  pierced  than  ordinary  glass,  and  hence 
Leyden  jars  made  of  it  may  be  made  thinner,  and  so  will 
hold  a  greater  charge.  To  prevent  jars  from  being  pierced 
by  a  spark,  the  highest  part  of  the  inside  coating  should 
be  connected  across  by  a  strip  of  foil  or  a  metallic  disk 
to  the  central  wire. 

If  a  jar  is  desired  to  give  long  sparks,  there  must  be 


CHAP. 


LEYDEN  JARS 


75 


left  a  long  space  of  varnished  glass  above  the  top  of  the 
coatings. 

If  it  is  desired  to  accumulate  a  very  great  charge  of 
electricity,  a  number  of  jars  must  be  employed,  all  their 
inner  coatings  being  connected  together,  and  all  their 
outer  coatings  being  united.  This  arrangement  is  called 
a  battery  of  Leyden  jars,  or  Leyden  battery  (Fig.  45). 
As  it  has  a  large  capacity,  it  will  require  a  large  quantity 
of  electricity  to  charge  it  fully.  When  charged  it  pro- 
duces very  powerful  effects;  its  spark  will  pierce  glass 
readily,  and  every  care  must  be 
taken  to  avoid  a  shock  from  it 
passing  through  the  person,  as  it 
might  be  fatal.  The  "Universal 
Discharger "  as  employed  with  the 
Leyden  battery  is  shown  at  the 
right  of  the  figure. 

63.  Seat  of  the  Charge.  —  Ben- 
jamin Franklin  discovered  that  the 
charges   of   the    Leyden  jar  really 
reside  on  the  surface  of  the  glass, 
not  on  the  metallic  coatings.     This 
he  proved  by  means  of  a  jar  whose 
coatings   could  be   removed    (Fig. 
46).     The    jar    was    charged    and 
placed  upon   an   insulating  stand. 
The  inner  coating  was  then  lifted 
out,   and  the   glass   jar   was  then 
taken   out    of    the    outer    coating. 
Xeither   coating  was  found  to  be 
electrified  to   any   extent,   but  on 
again  putting  the  jar   together  it 

was  found  to  be  highly  charged.  The  charges  had  all  the 
time  remained  upon  the  inner  and  outer  surfaces  of  the 
glass  dielectric. 

64.  Dielectric  Strain.  —  Farady  proved  that  the  me- 
dium across  which  influence  takes  place  really  plays  an 


Fig.  46. 


76  ELECTKICITY   AND   MAGNETISM       PART  i 

important  part  in  the  phenomena.  It  is  now  known 
that  all  dielectrics  across  which  inductive  actions  are  at 
work  are  thereby  strained.*  Inasmuch  as  a  good  vacuum 
is  a  good  dielectric,  it  is  clear  that  it  is  not  necessarily 
the  material  particles  of  the  dielectric  substance  that  are 
thus  affected ;  hence  it  is  believed  that  electrical  pheno- 
mena are  due  to  stresses  and  strains  in  the  so-called 
"ether,"  the  thin  medium  pervading  all  matter  and  all 
space,  whose  highly  elastic  constitution  enables  it  to  con- 
vey to  us  the  vibrations  of  light  though  it  is  millions  of 
times  less  dense  than  air.  As  the  particles  of  bodies  are 
intimately  surrounded  by  ether,  the  strains  of  the  ether 
are  also  communicated  to  the  particles  of  bodies,  and  they 
too  suffer  a  strain.  The  glass  between  the  two  coatings 
of  tinfoil  in  the  Leyden  jar  is  actually  strained  or 
squeezed,  there  being  a  tension  along  the  lines  of  electric 
force.  When  an  insulated  charged  ball  is  hung  up  in  a 
room  an  equal  amount  of  the  opposite  kind  of  charge  is 
attracted  to  the  inside  of  the  walls,  and  the  air  between 
the  ball  and  the  walls  is  strained  (electrically)  like  the 
glass  of  the  Leyden  jar.  If  a  Leyden  jar  is  made  of  thin 
glass  it  may  give  way  under  the  stress;  and  when  a 
Leyden  jar  is  discharged  the  layer  of  air  between  the 
knob  of  the  jar  and  the  knob  of  the  discharging  tongs  is 
more  and  more  strained  as  they  are  approached  towards 
one  another,  till  at  last  the  stress  becomes  too  great,  and 
the  layer  of  air  gives  way,  and  is  "perforated"  by  the 
spark  that  discharges  itself  across.  The  existence  of  such 
stresses  enables  us  to  understand  the  residual  charge  of 
Leyden  jars  in  which  the  glass  does  not  recover  itself  all 
at  once,  by  reason  of  its  viscosity,  from  the  strain  to 
which  it  has  been  subjected.  It  must  never  be  for- 
gotten that  electric  force  acts  across  space  in  conse- 
quence of  the  transmission  of  stresses  and  strains  in  the 

*  In  the  exact  sciences  a  strain  means  an  alteration  of  form  or  volume 
due  to  the  application  of  a  stress.  A  stress  is  the  force,  pressure,  or  other 
agency  which  produces  a  strain. 


CHAP,  i  OTHER   SOURCES  77 

medium  with  which  space  is  filled.  In  every  case  we 
store  not  electricity  but  energy.  Work  is  done  in  push- 
ing electricity  from  one  place  to  another  against  the 
forces  which  tend  to  oppose  the  movement.  The  charg- 
ing of  a  Ley  den  jar  may  be  likened  to  the  operation  of 
bending  a  spring,  or  to  pumping  up  water  from  a  low 
level  to  a  high  one.  In  charging  a  jar  we  pump  exactly 
as  much  electricity  out  of  the  negative  side  as  we  pump 
into  the  positive  side,  and  we  spend  energy  in  so  doing. 
It  is  this  stored  energy  which  afterwards  reappears  in 
the  discharge. 


LESSON  VII.  —  Other  Sources  of  Electrification 

65.  It  was    remarked    at   the    close   of    Lesson   I. 
(p.  13)  that  friction  was  by  no  means  the  only  source 
of  electricity.     Some  of  the  other  sources  will  now  be 
named. 

66.  Percussion.  —  A  violent  blow  struck  by  one  sub- 
stance upon  another  produces  opposite  electrical  states 
on  the  two  surfaces.     It  is  possible  indeed  to  draw  up  a 
list  resembling  that  of  Art.  6,  in  such  an  order  that  each 
substance  will  take  a  -f  charge  on  being  struck  with  one 
lower  on  the  list. 

67.  Vibration.  —  Volpicelli   showed   that   vibrations 
set  up  within  a  rod  of  metal  coated  with  sulphur  or 
other   insulating   substance,   produced    a   separation    of 
electricities  at  the  surface  separating  the  metal  from  the 
non-conductor. 

68.  Disruption  and  Cleavage.  —  If  a  card  be  torn 
asunder  in  the  dark,  sparks  are  seen,  and  the  separated 
portions,  when  tested  with  an  electroscope,  will  be  found 
to  be  electrical.     The  linen  faced  with   paper  used  in 
making  strong  envelopes  and  for  paper  collars,  shows 
this  very  well.     Lumps  of  sugar,  crunched  in  the  dark 
between  the  teeth,  exhibit  pale  flashes   of  light.     The 


78  ELECTRICITY   AND   MAGNETISM       PART  i 

sudden  cleavage  of  a  sheet  of  mica  also  produces  sparks, 
and  both  laminae  are  found  to  be  electrified. 

69.  Crystallization  and   Solidification.  —  Many   sub- 
stances, after  passing  from  the  liquid  to  the  solid  state, 
exhibit  electrical  conditions.     Sulphur  fused  in  a  glass 
dish  and  allowed  to  cool  is  violently  electrified,  as  may 
be  seen  by  lifting  out  the  crystalline  mass  with  a  glass 
rod.     Chocolate  also  becomes  electrical  during  solidifica- 
tion.    When  arsenic  acid  crystallizes  out  from  its  solu- 
tion in  hydrochloric  acid,  the  formation  of  each  crystal 
is  accompanied  by  a  flash  of  light,  doubtless  due  to  an 
electrical   discharge.     A   curious  case  occurs  when  the 
sulphate  of  copper  and  potassium  is  fused  in  a  crucible. 
It  solidifies  without  becoming  electrical,  but  on  cooling 
a  little  further  the   crystalline   mass   begins  to  fly  to 
powder  with  an  instant  evolution  of  electricity. 

70.  Combustion.  —  Volta    showed    that    combustion 
generated  electricity.     A  piece  of  burning  charcoal,  or  a 
burning  pastille,  such  as  is  used  for  fumigation,  placed 
in  connexion  with  the  knob  of  a  gold-leaf  electroscope, 
will  cause  the  leaves  to  diverge. 

71.  Evaporation.  —  The    evaporation    of    liquids    is 
often    accompanied    by   electrification,    the   liquid    and 
the  vapour  assuming  opposite  states,  though  apparently 
only   when  the  surface  is   in   agitation.     A  few  drops 
of   a  solution  of  sulphate  of  copper  thrown  into  a  hot 
platinum  crucible  produce  violent  electrification  as  they 
evaporate. 

72.  Atmospheric    Electricity.  —  The    atmosphere    is 
found  to  be  always  electrified  relatively  to  the  earth : 
this  is  due,  in  part  possibly,  to  evaporation  going  on 
over  the  oceans.     The  subject  of  atmospheric  electricity 
is  treated  of  separately  in  Lesson  XXV. 

73.  Pressure.  —  A  large  number  of  substances  when 
compressed  exhibit  electrification  on  their  surface.     Thus 
cork    becomes   -f   when   pressed    against    amber,   gutta- 
percha,   and   metals;   while   it  takes  a  —  charge  when 


CHAP,  i  PYRO-ELECTRICITY  79 

pressed  against  spars  and  animal  substances.  Peclet 
found  the  degree  of  electrification  produced  by  rubbing 
two  substances  together  to  be  independent  of  the  pressure 
and  of  the  size  of  the  surfaces  of  contact,  but  depended 
upon  the  materials  and  on  the  velocity  with  which  they 
moved  over  one  another.  Rolling  contact  and  sliding 
friction  produced  equal  effects. 

74.  Pyro-electricity.  —  There  are  certain  crystals 
which,  while  being  heated  or  cooled,  exhibit  electrical 
charges  at  certain  regions  or  poles.  Crystals  thus  elec- 
trified by  heating  or  cooling  are  said  to  be  pyro-electric. 
Chief  of  these  is  the  Tourmaline,  whose  power  of  attract- 
ing light  bodies  to  its  ends  after  being  heated  has  been 
known  for  some  centuries.  It  is  alluded  to  by  Theo- 
phrastus  and  Pliny  under  the  name  of  Lapis  Lyncurius. 
Tourmaline  is  a  hard  mineral,  semi-transparent  when 
cut  into  thin  slices,  and  of  a  dark  green  or  brown  colour, 
but  looking  perfectly  black  and  opaque  in  its  natural 
condition,  and  possessing  the  power  of  polarizing  light. 
It  is  usually  found  in  slightly  irregular  three-sided 
prisms  which,  when  perfect,  are  pointed  at  both  ends. 
It  belongs  to  the  "hexagonal"  system  of  crystals,  but 
is  only  hemihedral,  that  is  to  say,  has  the  alternate 
faces  only  developed.  Its  form  is  given  in  Fig.  47,  where 
a  general  view  is  first  shown,  the  two  ends  A  and  B 
being  depicted  in  separate  plans.  These  two  ends  differ 
slightly  in  shape.  Each  is  made  up  of  three  sloping  faces 
terminating  in  a  point.  But  at  A  the  edges  between 
these  faces  run  down  to  the  corners  of  the  prism,  while 
in  B  the  edges  between  the  terminal  faces  run  down  to 
the  middle  points  of  the  long  faces  of  the  prism.  The 
end  A  is  known  as  the  analogous  pole,  and  B  as  the 
antilogous  pole.  While  the  crystal  is  rising  in  tempera- 
ture A  exhibits  -f  electrification,  B  —  ;  but  if,  after  hav- 
ing been  heated,  it  is  allowed  to  cool,  the  polarity  is 
reversed ;  for  during  the  time  that  the  temperature 
is  falling  B  is  +  and  A  is  — .  If  the  temperature  is 


80 


ELECTRICITY   AND   MAGNETISM        PART  i 


steady  DO  such  electrical  effects  are  observed  either  at 
high  or  low  temperatures ;  and  the  phenomena  cease  if 
the  crystal  be  warmed  above  150°  C.  This  is  not,  how- 
ever, due  to  the  crystal  becoming  a  conductor  at  that 
temperature;  for  its  resistance  at  even  higher  tempera- 
tures is  still  so  great  as  to  make  it  practically  a  non- 
conductor. A  heated  crystal  of  tourmaline  suspended 
by  a  silk  fibre  may  be  attracted  and  repelled  by  electri- 
fied bodies,  or  by  a  second  heated  tourmaline ;  the  two 
similar  poles  repelling  one  another,  while  the  two  poles 


ill 


^^\~~/'<?<y-''_^ 

-s 

Y          \\\ 
\ 

1 

'[Too 

\ 

0'° 

i 

AJ 

V'' 

r.  47. 


Fig.  43. 


of  opposite  form  attract  one  another.  If  a  crystal  be 
broken  up,  each  fragment  is  found  to  possess  also  an 
analogous  and  an  antilogous  pole. 

Many  other  crystals  beside  the  tourmaline  are  more 
or  less  pyro-electric.  Amongst  these  are  silicate  of  zinc 
("electric  calamine"),  boracite,  cane-sugar,  quartz,  tar- 
trate  of  potash,  sulphate  of  quinine,  and  several  others. 
Boracite  crystallizes  in  the  form  shown  in  Fig.  48,  which 
represents  a  cube  having  four  alternate  corners  truncated. 
The  corners  not  truncated  behave  as  analogous  poles,  the 
truncated  ones  as  antilogous.  When  a  natural  hexagonal 
prism  of  quartz  is  heated  its  six  edges  are  found  to  be  + 
and  —  in  alternate  order. 


CHAP.    I 


PIEZO-ELECTRICITY 


81 


75.  Piezo-electricity.  —  In   certain   crystals   pressure 
in   a  particular   direction    may  produce    electrification. 
Haiiy  found  that  a  crystal  of  calcspar  pressed  between  the 
dry  fingers,  so  as  to  compress  it  along  the  blunt  edges  of 
the  crystal,  became  electrical,  and  that  it  retained  its 
electricity  for  some  days.     He  even  proposed  to  employ  a 
squeezed  suspended  crystal  as  an  electroscope.    A  similar 
property  is   alleged  of  mica, 

topaz,  and  fluorspar.  If  two 
opposite  edges  of  a  hexagonal 
prism  of  quartz  are  pressed 
together,  one  becomes  +  ,  the 
other  — .  Pressure  also  pro- 
duces opposite  kinds  of  electri- 
fication at  opposite  ends  of  a 
crystal  of  tourmaline,  and  of 
other  crystals  of  the  class 
already  noticed  as  possessing 
the  peculiarity  of  skew-sym- 
metry or  hemihedry  in  their 
structure.  Piezo-electricity  is 
the  name  given  to  this  branch 
of  the  science.  It  is  known 
that  skew-symmetry  of  struc- 
ture is  dependent  on  molecular 
constitution ;  and  it  is  doubt- 
less the  same  peculiarity  which 
determines  the  pyro-electric 
and  piezo-electric  properties, 
as  well  as  the  optical  behaviour 
of  these  crystals  in  polarized 
light. 

76.  Animal  Electricity.— 
Several   species    of    creatures 

inhabiting  the  water  have  the  power  of  producing 
electric  discharges  physiologically.  The  best  known  of 
these  creatures  are  the  Torpedo,  the  Gymnotus,  and  the 


Fig.  49. 


ELECTRICITY   AND   MAGNETISM       PART  i 

Silurus.  The  Raia  Torpedo,*  or  electric  ray,  of  which 
there  are  three  species  inhabiting  the  Mediterranean  and 
Atlantic,  is  provided  with  an  electric  organ  on  the  back 
of  its  head,  as  shown  in  Fig.  49.  This  organ  consists  of 
laminae  composed  of  polygonal  cells  to  the  number  of  800 
or  1000,  or  more,  supplied  with  four  large  bundles  of 
nerve  fibres ;  the  under  surface  of  the  fish  is  — ,  the  upper 
-1- .  In  the  Gymnotus  electricus,  or  Surinam  eel  (Fig.  50), 
the  electric  organ  goes  the  whole  length  of  the  body  from 
tail  to  head.  Humboldt  gives  a  lively  account  of  the 


Fig.  50. 

combats  between  the  electric  eels  and  the  wild  horses, 
driven  by  the  natives  into  the  swamps  inhabited  by  the 
Gymnotus.  It  is  able  to  give  a  most  terrible  shock,  and 
is  a  formidable  antagonist  when  it  has  attained  its  full 
length  of  5  or  6  feet.  In  the  Silurus  the  current  flows 
from  head  to  tail. 

Nobili,  Matteucci,  and  others,  have  shown  that  nerve- 
excitations  and  muscular  contractions  of  human  beings 
also  give  rise  to  feeble  discharges  of  electricity. 

77.  Electricity  of  Vegetables.  — Buff  thought  he 
detected  electrification  produced  by  plant  life ;  the  roots 
and  juicy  parts  being  negatively,  and  the  leaves  posi- 
tively, electrified.  The  subject  has,  however,  been  little 
investigated. 

*  It  is  a  curious  point  that  the  Arabian  name  for  the  torpedo,  rand. 
signifies  lightning.  This  is  perhaps  not  so  curious  as  that  the  Electra  of 
the  Homeric  legends  should  possess  certain  qualities  that  would  tend  to 
suggest  that  she  is  a  personification  of  the  lightning.  The  resemblance 
between  the  names  electro,  and  electron  (amber)  cannot  be  accidental. 


CHAP,  i      ELECTRIFICATION  BY   CONTACT 


83 


78.  Thermo-electricity.  —  Heat   applied  at  the  junc- 
tion of  two  dissimilar  metals  produces  a  flow  of  elec- 
tricity across  the  junction.     This  subject  is  discussed  in 
Lesson  XXXV.  on  Thermo-electric  Currents. 

79.  Contact  of    Dissimilar  Metals.  —  Volta  showed 
that  the  contact  of  two  dissimilar  metals  in  air  produced 
opposite     kinds     of 

electrification,  one 
becoming  positively, 
and  the  other  neg- 
atively, electrified. 
This  he  proved  in 
several  ways,  one  of 
the  most  conclusive 
proofs  being  that 
afforded  by  his  con- 
densing electroscope. 
This  consisted  of  a 
gold-leaf  electroscope 
combined  with  a 
small  condenser.  A 
metallic  plate  formed 
the  top  of  the  electro- 
scope, and  on  this 
was  placed  a  second 
metallic  plate  fur- 
nished with  a  handle,  and  insulated  from  the  lower  one 
by  being  well  varnished  at  the  surface  (Fig.  51).  As  the 
capacity  of  such  a  condenser  is  considerable,  a  very  feeble 
source  may  supply  a  quantity  of  electricity  to  the  con- 
denser without  materially  raising  its  potential,  or  causing 
the  gold  leaves  to  diverge.  But  if  the  upper  plate  be  lifted, 
the  capacity  of  the  lower  plate  diminishes  enormously, 
and  the  potential  of  its  charge  rises  as  shown  by  the 
divergence  of  the  gold  leaves.*  To  prove  by  the  con- 

*  Formerly,  this  action  was  accounted  for  by  saying  that  the  electricity 
which  was  "  bound  "  when  the  plates  of  the  condenser  were  close  together, 


84  ELECTRICITY  AND   MAGNETISM       PART  i 

densing  electroscope  that  contact  of  dissimilar  metals  does 
produce  electrification,  a  small  compound  bar  made  of 
two  dissimilar  metals  —  say  zinc  and  copper  —  soldered 
together,  is  held  in  the  moist  hand,  and  one  end  of  it  is 
touched  against  the  lower  plate,  the  upper  plate  being 
placed  in  contact  with  the  ground  or  touched  with  the 
finger.  When  the  two  opposing  charges  have  thus  col- 
lected in  the  condenser  the  upper  plate  is  removed,  and 
the  diverging  of  the  gold  leaves  shows  the  presence  of 
a  free  charge,  which  can  afterwards  be  examined  to  see 
whether  it  be  +  or  — .  Instead  of  employing  the  copper- 
zinc  bar,  a  single  voltaic  cell  may  be  connected  by  copper 
wires  to  the  two  plates.  For  a  long  time  the  existence  of 
this  electrification  by  contact  was  denied,  or  rather  it  was 
declared  to  be  due  (when  occurring  in  voltaic  combina- 
tions such  as  are  described  in  Lesson 
XIII.)  to  chemical  actions  going  on; 
whereas  the  real  truth  is  that  the 
electricity  of  contact  and  the  chemical 
action  are  both  due  to  molecular  con- 
ditions of  the  substances  which  come 
into  contact  with  one  another,  though 
we  do  not  yet  know  the  precise  nature 
of  the  molecular  conditions  which  give 
rise  to  these  two  effects.  Later  experiments,  especially 
those  made  with  the  modern  delicate  electrometers 
of  Lord  Kelvin,  put  beyond  doubt  the  reality  of 
Volta's  discovery.  One  simple  experiment  explains 
the  method  adopted.  A  thin  strip  or  needle  of  metal 
is  suspended  so  as  to  turn  about  a  point  C.  It  is 
electrified  from  a  known  source.  Under  it  are  placed 
(Fig.  52)  two  semicircular  disks,  or  half-rings  of  dissimilar 


becomes  "free"  when  the  top  plate  is  lifted  up;  the  above  is,  however,  a 
more  scientific  and  more  accurate  way  of  saying  the  same  thing.  The 
student  who  is  unable  to  reconcile  these  two  ways  of  stating  the  matter 
should  read  again  Articles  40  and  55,  on  pp.  4G  and  G8.  A  much  more  sensi- 
tive apparatus  to  show  the  effect  is  the  quadrant  electrometer  (Art.  288). 


CHAI>.  i       CONTACT  SERIES  OF  METALS  85 

metals.  Neither  attracts  or  repels  the  electrified  needle 
until  the  two  are  brought  into  contact,  or  connected  by  a 
third  piece  of  metal,  when  the  needle  immediately  turns, 
being  attracted  by  the  one  that  is  oppositely  electrified,  and 
repelled  by  the  one  that  is  electrified  similarly  with  itself. 
80.  Contact  Series  of  Metals  (in  Air).  —  Volta 
found,  moreover,  that  the  differences  of  electric  potential 
between  the  different  pairs  of  metals  were  not  all  equal. 
Thus,  while  zinc  and  lead  were  respectively  +  and  —  to 
a  slight  degree,  he  found  zinc  and  silver  to  be  respec- 
tively +  and  —  to  a  much  greater  degree.  He  was  able 
to  arrange  the  metals  in  a  series  such  that  each  one 
enumerated  became  positively  electrified  when  placed  in 
contact  in  air  with  one  below  it  in  the  series.  Those 
in  italics  are  added  from  observations  made  since  Volta's 
time  — 

+  Sodium,  Copper, 

Magnesium,  Silver, 

Zinc,  Gold, 

Lead,  Platinum, 

Tin,  —  Graphite  (Carbon). 

Iron, 

Though  Volta  gave  rough  approximations,  the  actual 
numerical  values  of  the  differences  of  potential  in  air  for 
different  pairs  of  metals  have  only  lately  been  measured 
by  Ayrton  and  Perry,  a  few  of  whose  results  are  tabu- 
lated here  — 

Difference  of  Potential 

(volts). 
Zinc  ,  ,210 


^  ...         -069 

Tin 

__  -313 

Iron 


•146 
I  ...          -238 

\  .          .          '113 

Carbon 


Copper 
Platinum 


86  ELECTRICITY   AND  MAGNETISM       PART  i 

The  difference  of  potential  between  zinc  and  carbon 
is  the  same  as  that  obtained  by  adding  the  successive 
differences,  or  1-09  volts.*  Volta's  observations  may 
therefore  be  stated  in  the  following  generalized  form, 
known  as  Volta's  Law.  The  difference  of  potential  be- 
tween any  two  metals  is  equal  to  the  sum  of  the  differences 
of  potentials  between  the  intervening  metals  in  the  contact- 
series. 

It  is  most  important  to  notice  that  the  order  of  the 
metals  in  the  contact-series  in  air  is  almost  identical 
with  that  of  the  metals  arranged  according  to  their 
electro-chemical  power,  as  calculated  from  their  chemical 
equivalents  and  their  heat  of  combination  with  oxygen 
(see  Table,  Art.  489).  From  this  it  would  appear  that 
the  difference  of  potentials  between  a  metal  and  the  air 
that  surrounds  it  measures  the  tendency  of  that  metal 
to  become  oxidized  by  the  air.  If  this  is  so,  and  if  (as 
is  the  case)  the  air  is  a  bad  conductor  while  the  metals 
are  good  conductors,  it  ought  to  follow  that  when  two 
different  metals  touch  they  equalize  their  own  potentials 
by  conduction  but  leave  the  films  of  air  that  surround 
them  at  different  potentials.  All  the  exact  experiments 
yet  made  have  measured  the  difference  of  potentials  not 
between  the  metals  themselves,  but  between  the  air  near 
one  metal  and  that  near  another  metal.  It  is  certain 
that  while  in  air  iron  is  positive  to  copper,  but  in  an 
atmosphere  of  sulphuretted  hydrogen,  iron  is  negative  to 
copper.  Mr.  John  Brown  has  lately  demonstrated  the 
existence  on  freshly-cleaned  metal  surfaces  of  films  of 
liquid  or  condensed  gases,  and  has  shown  that  polished 
zinc  and  copper,  when  brought  so  near  that  their  films 
touch,  will  act  as  a  battery. 

81.  Contact  Actions.  —  A  difference  of  potential  is 
also  produced  by  the  contact  of  two  dissimilar  liquids  with 
one  another. 

*  For  the  definition  of  the  volt,  or  unit  of  difference  of  potential,  sec- 
Art.  254. 


CHAP,  i  CONTACT  ACTIONS  87 

A  liquid  and  a  metal  in  contact  with  one  another  also 
exhibit  a  difference  of  potential,  and  if  the  metal  tends 
to  dissolve  into  the  liquid  chemically  there  will  be  an 
electromotive  force  acting  from  the  metal  toward  the 
liquid. 

The  thermo-electric  difference  of  potential  at  a  junc- 
tion of  two  metals  is  a  true  contact  difference.  It  is 
measured  by  the  amount  of  heat  produced  (see  Peltier- 
effect,  Art.  420)  by  passing  a  current  of  electricity  in  the 
reverse  direction  through  the  junction. 

A  hot  metal  placed  in  contact  with  a  cold  piece  of 
the  same  metal  also  produces  a  difference  of  potential, 
electrical  separation  taking  place  across  the  surface  of 
contact. 

Lastly,  it  has  been  shown  by  Professor  J.  J.  Thomson 
that  the  surface  of  contact  between  two  non-conducting 
substances,  such  as  sealing-wax  and  glass,  is  the  seat  of  a 
permanent  difference  of  potentials. 

82.  Magneto-electricity. — Electric  currents  flowing 
along  in  wires  can  be  obtained  from  magnets  by  moving 
closed  conducting  circuits  in  their  neighbourhood.     This 
source  is  dealt  with  in  Art.  222,  Lesson  XVIII. 

83.  Summary.  —  We  have    seen   in   the   preceding 
paragraphs  how  almost  all  conceivable  agencies  may  pro- 
duce electrification  in  bodies.     The  most  important  of 
these  are  friction,  heat,  chemical  action,  magnetism,  and 
the  contact  of  dissimilar  substances.     We  noted  that  the 
production   of   electricity  by  friction   depended  largely 
upon  the  molecular  condition  of  the  surfaces.     We  may 
here  add  that  the  difference  of  potentials  produced  by 
contact  of   dissimilar  substances   also  varies  with  the 
temperature  and  with  the  nature  of  the  medium  (air, 
vacuum,   etc.)    in  which    the    experiments    are   made. 
Doubtless  this  source  also  depends  upon  the  molecular 
conditions  of  dissimilar  substances  being  different ;  the 
particles   at  the   surfaces  being  of   different  sizes   and 
shapes,  and  vibrating  with  different  velocities  and  with 


ELECTRICITY  AND   MAGNETISM        PART  i 

different  forces.  There  are  (see  Art.  10)  good  reasons 
for  thinking  that  the  electricity  of  friction  is  really  due 
to  electricity  of  contact,  excited  at  successive  portions  of 
the  surfaces  as  they  are  moved  over  one  another.  But  of 
the  molecular  conditions  of  bodies  which  determine  the 
production  of  electrification  where  they  come  into  contact, 
little  or  nothing  is  yet  known. 


CHAPTER  II 

MAGNETISM 

LESSON  VIII.  —  Magnetic  Attraction  and  Repulsion 

84.  Lodestones   or    Natural    Magnets.  —  The   name 
Magnet  (Magnes  Lapis)  was  given  by  the   ancients  to 
certain  hard  black  stones  found  in  various  parts  of  the 
world,  notably  at  Magnesia  in  Asia  Minor,  which  pos- 
sessed the  property  of  attracting  to  them  small  pieces 
of  iron.     This  magic  property,  as  they  deemed  it,  made 
the  magnet-stone  famous  ;  but  it  was  not  until  the  tenth 
or  twelfth  century  that  such  stones  were  discovered  to 
have   the   still   more   remarkable    property  of  pointing 
north  and  south  when  hung  up  by  a  thread.     This  prop- 
erty was  turned  to  advantage  in  navigation,  and  from 
that  time  the  magnet  received  the  name  of  Lodestone  * 
(or  "leading-stone  ").     The  natural  magnet  or  lodestone 
is  an  ore  of  iron,  known  to  mineralogists  as  magnetite  and 
having  the   chemical  composition   Fe3O4.     This   ore  is 
found  in  quantities  in  Sweden,  Spain,  the  Isle  of  Elba, 
Arkansas,   and  other  parts   of   the   world,   though   not 
always  in  the  magnetic  condition.     It  frequently  occurs 
in  crystals  ;  the  usual  form  being  the  regular  octahedron. 

85.  Artificial  Magnets.  —  If  apiece  of  hard  iron  be 
rubbed  with  a  lodestone,  it  will  be  found  to  have  also 

*  The  common  spelling  loadstone  is  due  to  misapprehension. 


90  ELECTRICITY   AND    MAGNETISM        PART  i 

acquired  the  properties  characteristic  of  the  stone  ;  it 
will  attract  light  bits  of  iron,  and  if  hung  up  by  a 

thread  it  will  point 
north  and  south. 
Savery,  in  1729, 
first  showed  how 
much  more  reten- 
tive of  magnetism 
hardened  steel  is 
than  mere  iron. 
Figs.  53  and  54 

Figs.  53  and  54. 

represent  a  natural 

lodestone  and  an  artificial  magnet  of  steel,  each  of  which 
has  been  dipped  into  iron-filings  ;  the  filings  are  attracted 
and  adhere  in  tufts. 

86.  Writings  of  Dr.  Gilbert.  —  This  was  all,  or  nearly 
all,  that  was  known   of  the   magnet  until   1600,  when 
Dr.  Gilbert  published  a  large  number  of  magnetic  dis- 
coveries in  his  famous  work  De  Magnete.     He  observed 
that  the  attractive  power  of  a  magnet  appears  to  reside 
at  two  regions,   and    in   a  long-shaped    magnet    these 
regions,  or  poles,  are  usually  at  the  ends  (see  Figs.  53 
and  54).     The  portion  of  the  magnet  which  lies  between 
the  two  poles  is  apparently  less  magnetic,  and  does  not 
attract  iron-filings  so  strongly;   and  all  round  the  mag- 
net, halfway  between  the  poles,  there  is  no  attraction 
at   all.     This  region   Gilbert  called  the  equator  of  the 
magnet,  and  the  imaginary  line  joining  the  poles  he 
termed  the  axis. 

87.  Magnetic   Needle.  —  To   investigate   more  fully 
the   magnetic    forces    a  magnetic    needle    is   employed. 
This  consists  (Fig.  55)  of  a  light  needle  cut  out  of  steel, 
and  fitted  with  a  little  cap  of  brass,  glass,  or  agate,  by 
means  of  which  it  can  be  hung  upon  a  sharp  point,  so 
as   to  turn   with   very   little    friction.      It    is   rendered 
magnetic  by  being  rubbed  upon  a  magnet ;   and  when 
thus  magnetized  it  will   turn   into   the  north-and-south 


CHAP.    II 


MAGNETIC   ATTRACTIONS 


91 


position,  or,  as  we  should  say,  will  set  itself  in  the 
"magnetic  meridian"  (Art.  151).  The  compass  sold 
by  opticians  consists 
of  such  a  needle 
balanced  above  a 
card  marked  with 
"points  of  the  com- 
pass." 

88.  Magnetic 
Attractions  and 
Repulsions.  —  If 
we  take  a  magnet 
(either  natural  or 
artificial)  in  our 
hand  and  present 
the  two  "poles"  of 
it  successively  to  the 
north-pointing  end 
of  a  magnetic  needle, 
we  shall  observe  that 


Fig.  55. 


one  pole  of  the  magnet  attracts  it,  while  the  other  repels 
it  (Fig.  56).  Repeating  the  experiment  on  the  south- 
pointing  end  of 
the  magnetic 
needle,  we  find 
that  it  is  repelled 
by  one  pole  and 
attracted  by  the 
other ;  and  that 
the  same  pole 

N     ~"  """""""* 


which  attracts  the 
north  -pointing 
end  of  the  needle 
repels  the  south- 
pointing  end. 

Tf    we    try   a   similar  experiment   on   the   magnetic 
needle,  using  for  a  magnet  a  second  magnetized  needle 


92  ELECTRICITY   AND   MAGNETISM        PART  i 

which  has  previously  been  suspended,  and  which  has  its 
north-pointing  end  marked  to  distinguish  it  from  the 
south-pointing  end,  we  shall  discover  that  the  N-pointing 
pole  repels  the  N-pointing  pole,  and  that  the  S-pointing 
pole  repels  the  S-pointing  pole  ;  but  that  a  N-pointing  pole 
attracts  and  is  attracted  by  a  S-pointing  pole. 

89.  Two  Kinds  of  Magnetic  Poles.  —  There  would 
therefore  appear  to  be  two  opposite  kinds  of  magnetism, 
or  at  any  rate  two  opposite  kinds  of  magnetic  poles, 
which  attract  or  repel  one  another  in  very  much  the 
same  fashion  as  the  two  opposite  kinds  of  electrification 
do ;  and  one  of  these  kinds  of  magnetism  appears  to  have 
a  tendency  to  move  toward  the  north  and  the  other  to 
move  toward  the  south.  It  has  been  proposed  to  call 
these  two  kinds  of  magnetism  "north-seeking  magnet- 
ism "  and  "  south-seeking  magnetism,"  but  for  our  pur- 
pose it  is  sufficient  to  distinguish  between  the  two  kinds 
of  poles.  In  common  parlance  the  poles  of  a  magnet  are 
called  the  "  North  Pole  "  and  "  South  Pole  "  respectively, 
and  it  is  usual  for  the  makers  of  magnets  to  mark  the 
N-pointing  pole  with  a  letter  N.  It  is  therefore  some- 
times called  the  "  marked  "  pole,  to  distinguish  it  from 
the  S-pointing  or  "unmarked  "  pole.  We  shall,  to  avoid 
any  doubt,*  call  that  pole  of  a  magnet  which  would, 

*  It  is  necessary  to  be  precise  on  this  point,  as  there  is  some  confusion 
in  the  existing  text-books.  The  cause  of  the  confusion  is  this :  —  If  the 
north-pointing  pole  of  a  needle  is  attracted  by  magnetism  residing  near  the 
North  Pole  of  the  earth,  the  law  of  attraction  (that  unlike  poles  attract) 
shows  us  that  these  two  poles  are  really  magnetically  of  opposite  kinds. 
Which  are  we  then  to  call  north  magnetism  ?  That  which  is  at  the  N  pole 
of  the  earth  ?  If  so,  we  must  say  that  the  N-pointing  pole  of  the  needle 
contains  south  magnetism.  And  if  we  call  that  north  magnetism  which 
points  to  the  north,  then  we  must  suppose  the  magnetic  pole  at  the  north 
pole  of  the  earth  to  have  south  magnetism  in  it.  In  either  case  there  is 
then  a  difficulty.  The  Chinese  and  the  French  call  the  N-pointing  pole  of 
the  needle  a  south  pole,  and  the  S-pointing  pole  a  north  pole.  Lord  Kel- 
vin also  calls  the  N-pointing  pole  a  "  True  South  "  pole.  But  common 
practice  goes  the  other  way,  and  calls  the  N-pointing  pole  of  a  magnet  its 
"North"  pole.  For  experimental  purposes  it  is  usual  to  paint  the  two 
poles  of  a  magnet  of  different  colours,  the  N-seeking  pole  being  coloured 


CHAP.  IT  POLAR   EFFECTS  93 

if  the  magnet  were  suspended,  tend  to  turn  to  the  north, 
the  "  North-seeking "  pole,  and  the  other  the  "  South- 
seeking  "  pole. 

We  may  therefore  sum  up  our  observations  in  the  con- 
cise statement:  Like  magnetic  poles  repel  one  another ;  un- 
like poles  attract  one  another.  This  we  may  call  the  first 
law  of  magnetism.  As  with  the  electric  attractions  and 
repulsions  of  rubbed  bodies,  so  with  these  magnetic 
attractions  and  repulsions  the  effects  are  due,  as  we  shall 
see,  to  stresses  in  the  intervening  medium. 

90.  The  two  Poles  inseparable.  —  It  is  impossible  to 
obtain  a  magnet  with  only  one  pole.     If  we  magnetize 
a  piece  of  steel  wire,  or  watch  spring,  by  rubbing  it  with 
one  pole  of  a  magnet,  we  shall  find  that  still  it  has  two 
poles  —  one  N-seeking,  the  other  S-seeking.     And  if  we 
break  it  into  two  parts,  each  part  will  still  have  two  poles 
of  opposite  kinds. 

91.  Magnetic  Force.  —  The  force  with  which  a  mag- 
net attracts  or  repels  another  magnet,  or  any  piece  of 
iron   or  steel,  we  shall  call  magnetic  force.*     The  force 
exerted  by  a  magnet  upon  a  bit 

of  iron  or  on  another  magnet  is 

not  the  same  at  all  distances,  the 

force    being    greater    when    the 

magnet  is  nearer,  and  less  when 

the  magnet  is  farther  off.     (See 

Art.   128,   on  laws   of    magnetic  ~ 

force.) 

Whenever  a  force  acts  thus  between  two  bodies,  it  acts 
on  both  of  them,  tending  to  move  both.  A  magnet  will 
attract  a  piece  of  iron,  and  a  piece  of  iron  will  attract 
a  magnet.  This  was  shown  by  Sir  Isaac  JSTewton,  who 

red  and  the  S-seeking  pole  blue;  but  here  again,  strangely  enough, 
authorities  differ,  for  in  the  collections  of  apparatus  at  the  Koyal  Institu- 
tion and  Royal  School  of  Mines,  the  colours  are  used  in  exactly  the  opposite 
way  to  this,  which  is  due  to  Airy. 

*  See  footnote  on  "Force,"  Art.  169. 


94  ELECTRICITY  AND   MAGNETISM        PART  i 

fixed  a  magnet  upon  a  piece  of  cork  and  floated  it  in  a 
basin  of  water  (Fig.  57),  and  found  that  it  moved  across 
the  basin  when  a  piece  of  iron  was  held  near.  A  com- 
pass needle  thus  floated  turns  round  and  points  north 
and  south ;  but  it  does  not  rush  towards  the  north  as  a 
whole,  nor  towards  the  south.  The  reason  of  this  will 
be  explained  later,  in  Art.  129. 

Gilbert  suggested  that  the  force  of  a  magnet  might  be 
measured  by  making  it  attract  a  piece  of  iron  hung  to 
one  arm  of  a  balance,  weights  being  placed  in  the  scale- 
pan  hanging  to  the  other  arm ;  and  he  found,  by  hanging 
the  magnet  to  the  balance  and  placing  the  iron  beneath 
it,  that  the  effect  produced  was  the  same.  The  action 
and  reaction  are  then  equal  for  magnetic  forces. 

92.  Magnetic  Substances.  —  A  distinction  was  drawn 
by  Gilbert  between  magnets  and  magnetic  substances.     A 
magnet  attracts  only  at  its  poles,  and  they  possess  oppo- 
site properties.     But  a  lump  of  iron  will  attract  either 
pole  of  the  magnet,  no  matter  what  part  of  the  lump  be 
presented    to   the   magnet.     It   has    no   distinguishable 
fixed  "  poles,"  and  no  magnetic  "  equator."     A  true  mag- 
net has  poles,  one  of  which  is  repelled  by  the  pole   of 
another  magnet. 

93.  Other  Magnetic   Metals.  —  Later    experimenters 
have  extended  the  list  of  substances  which  are  attracted 
by  a  magnet.     In  addition  to  iron  (and  steel)  the  follow- 
ing metals  are  recognized  as  magnetic  :  — 

Nickel.  Chromium. 

Cobalt.  Cerium, 

and  a  few  others.  But  only  nickel  and  cobalt  are  at  all 
comparable  with  iron  and  steel  in  magnetic  power,  and 
even  they  are  very  far  inferior.  Other  bodies,  sundry 
salts  of  iron  and  other  metals,  paper,  porcelain,  and 
oxygen  gas,  are  also  very  feebly  attracted  by  a  powerful 
magnet. 


CHAP,  ii        INDUCTION  OF   MAGNETISM  95 

94.  Diamagnetism.  —  A  number  of  bodies,  notably 
bismuth,  antimony,  phosphorus,  and  copper,  are  appar- 
ently repelled  from  the  poles  of  a  magnet.     Such  bodies 
are  called  diamagnetic  bodies;   a  fuller  account  of  them 
will  be  found  in  Lesson  XXIX. 

95.  The  Earth  a  Magnet.  —  Jhe  greatest  of  Gilbert's 
discoveries  was  that  of  the  inherent  magnetism  of  the 
earth.     The  earth  is  itself  a  great  magnet,  whose  "poles" 
coincide  nearly,  but  not   quite,  with  the   geographical 
north  and  south  poles,  and  therefore  it  causes  a  freely- 
suspended  magnet  to  turn  into  a  north-and-south  posi- 
tion.    Gilbert  had  some  lodestones  cut  to  the  shape  of 
spheres  to  serve  as  models  of  the  globe  of  the  earth. 
Such  a  globular  magnet  he  called  a  terrella.     He  found 
that  small  magnets  turned  toward  the  poles  of  the  ter- 
rella, and  dip,  as  compass-needles  do,  toward  the  earth. 

The  subject  of  Terrestrial  Magnetism  is  treated  of  in 
Lesson  XII.  It  is  evident  from  the  first  law  of  magnet- 
ism that  the  magnetic  condition  of  the  northern  regions 
of  the  earth  must  be  the  opposite  to  that  of  the  north- 
seeking  pole  of  a  magnetized  needle.  Hence  arises  the 
difficulty  alluded  to  on  page  92. 

96.  Induction  of  Magnetism.  —  Magnetism  may  be 
communicated  to  a  piece  of  iron  without  actual  contact 


Fig.  58. 

with  a  magnet.  If  a  short,  thin  unmagnetized  bar  of 
iron  be  placed  near  some  iron  filings,  and  a  magnet  be 
brought  near  to  the  bar,  the  presence  of  the  magnet  will 
induce  magnetism  in  the  iron  bar,  and  it  will  now  attract 
the  iron  filings  (Fig.  58).  This  inductive  action  is  very 
similar  to  that  observed  in  Lesson  III.  to  take  place  when 
a  non-electrified  body  was  brought  under  the  influence  of 


96  ELECTRICITY  AND   MAGNETISM       PART  i 

an  electrified  one.  The  analogy,  indeed,  goes  further 
than  this,  for  it  is  found  that  the  iron  bar  thus  magnet- 
ized by  induction  will  have  two  poles ;  the  pole  nearest 
to  the  pole  of  the  inducing  magnet  being  of  the  opposite 
kind,  while  the  pole  at  the  farther  end  of  the  bar  is 
of  the  same  kind  as  the  inducing  pole.  Those  bodies 
in  which  a  magnetizing  force  produces  a  high  degree  of 
magnetization  are  said  to  possess  a  high  permeability.  It 
will  be  shown  presently  that  magnetic  induction  takes 
place  along  certain  directions  called  lines  of  magnetic  in- 
duction, or  lines  of  magnetic  force,  which  may  pass  either 
through  iron  and  other  magnetic  media,  or  through  air, 
vacuum,  glass,  or  other  non-magnetic  media :  and,  since 
induction  goes  on  most  freely  in  bodies  of  high  magnetic 
permeability,  the  magnetic  lines  are  sometimes  (though 
not  too  accurately)  said  to  "  pass  by  preference  through 
magnetic  matter,"  or,  that  "magnetic  matter  conducts 
the  lines  of  force." 

97.  Attraction  across  Bodies.  —  If  a  sheet  of  glass, 
or  wood,  or  paper,  be  interposed  between  a  magnet  and 
the  piece  of  iron  or  steel  it  is  attracting,  it  will  still  at- 
tract it  as  if  nothing  were  interposed.  A  magnet  sealed 
up  in  a  glass  tube  still  acts  as  a  magnet.  Lucretius  found 
a  magnet  put  into  a  brass  vase  attracted  iron  filings 
through  the  brass.  Gilbert  surrounded  a  magnet  by  a 
ring  of  flames,  and  found  it  still  to  be  subject  to  magnetic 
attraction  from  without.  Across  water,  vacuum,  and  all 
known  substances,  the  magnetic  forces  will  act ;  with  the 
single  apparent  exception,  however,  that  magnetic  force 
will  not  act  across  a  screen  of  iron  or  other  magnetic 
material,  if  sufficiently  thick.  If  a  small  magnet  is  sus- 
pended inside  a  hollow  ball  made  of  iron,  no  outside 
magnet  will  affect  it.  The  reason  being  that  the  mag- 
netic lines  of  force  are  conducted  off  laterally  through 
the  iron  instead  of  penetrating  through  it.  A  hollow 
shell  of  iron  will  therefore  act  as  a  magnetic  cage,  and 
shield  the  space  inside  it  from  magnetic  influences. 


CHAl'.    II 


MAGNETIC   SCREENING 


07 


Fig.  59  illustrates  the  way  in  which  a  cylinder  of  soft 
iron  shields  the  space  interior  to  it  from  the  influence  of 
an  external  magnet.  A  compass  needle  placed  at  P  inside 
the  cylinder  is  not  affected  by  the  presence  of  the  magnet 
outside,  for  its  lines  of  magnetic  force  are  drawn  off 
laterally.  Similarly  a  magnet  inside  is  shielded  from 
affecting  outside  space. 

Although  magnetic  induction  takes  place  at  a  distance 
across  an  intervening  layer  of  air,  glass,  or  vacuum,  there 
is  no  doubt  that  the  intervening  medium  is  directly  con- 
cerned in  the  transmission  of  the  magnetic  force,  though 
the  true  medium  is  probably  the  "  ether  "  of  space  sur- 


Fig.  59. 

rounding  the  molecules  of  matter,  not  the  molecules 
themselves. 

We  now  can  see  why  a  magnet  should  attract  a  not- 
previously-magnetized  piece  of  iron;  it  first  magnetizes 
it  by  induction  and  then  attracts  it :  for  the  nearest  end 
will  have  the  opposite  kind  of  magnetism  induced  in  it, 
and  will  be  attracted  with  a  force  exceeding  that  with 
which  the  more  distant  end  is  repelled.  But  induction 
precedes  attraction. 

98-  Retention  of  Magnetization.  —  Not  all  magnetic 
substances  can  become  magnets  permanently.  Lode- 
stone,  steel,  and  nickel  retain  permanently  the  great 
part  of  the  magnetism  imparted  to  them.  Cast  iron 
and  many  impure  qualities  of  wrought  iron  also  retain 


ELECTRICITY   AND   MAGNETISM       PART  i 


magnetism  imperfectly.  The  softer  and  purer  a  speci- 
men of  iron  is,  the  more  lightly  is  its  residual  magnet- 
ism retained.  The  following  experiment  illustrates  the 
matter :  —  Let  a  few  pieces  of  iron  rod,  or  a  few  soft 
iron  nails  be  taken.  If  one  of  these  (see  Fig.  60)  be 
placed  in  contact  with  the  pole  of  a  permanent  steel 
magnet,  it  is  attracted  to  it,  and  becomes  itself  a  tempo- 
rary magnet.  Another  bit  of  iron  may  then  be  hung 
to  it,  and  another,  until  a  chain  of  four  or  five  pieces  is 
built  up.  But  if  the  steel  mag- 
net be  removed  from  the  top  of 
the  chain,  all  the  rest  drop  off, 
and  are  found  to  be  no  longer 
magnetic.  A  similar  chain  of 
steel  needles  may  be  formed,  but 
they  will  retain  permanently 
most  of  their  magnetism. 

It  will  be  found,  however,  that 
a  steel  needle  is  more  difficult  to 
magnetize  than  an  iron  needle 
of  the  same  dimensions.  It  is 
harder  to  get  the  magnetism  into  steel  than  into  iron, 
and  it  is  harder  to  get  the  magnetism  out  of  steel  than 
out  of  iron ;  for  the  steel  retains  the  magnetism  once 
put  into  it.  This  power  of  resisting  magnetization,  or 
demagnetization,  is  sometimes  called  coercive  force:  a 
much  better  term,  due  to  Lament,  is  retentivity.  The 
retentivity  of  hard-tempered  steel  is  great ;  that  of  soft 
wrought  iron  is  very  small.  The  harder  the  steel,  the 
greater  its  retentivity.  Form  affects  retentivity.  Elon- 
gated forms  and  those  shaped  as  closed  or  nearly  closed 
circuits  retain  their  magnetism  better  than  short  rods, 
balls,  or  cubes. 

99.  Theories  of  Magnetism.  —  The  student  will  not 
have  failed  to  observe  the  striking  analogies  between 
the  phenomena  of  attraction,  repulsion,  induction,  etc., 
of  magnetism  and  those  of  electricity.  Yet  the  two  sets 


CHAP,  ii     METHODS  OF   MAGNETIZATION  99 

of  phenomena  are  quite  distinct.  A  positively  electrified1 
body  does  not  attract  either  the  North-pointing  or  the 
South-pointing  pole  of  the  magnet  as  such;  in  fact,  it 
attracts  either  pole  quite  irrespective  of  its  magnetism, 
just  as  it  will  attract  any  other  body.  There  does  exist, 
indeed,  a  direct  relation  between  magnets  and  currents 
of  electricity,  as  will  be  later  explained.  There  is  none 
known,  however,  between  magnets  and  stationary  charges 
of  electricity. 

In  many  treatises  it  is  the  fashion  to  speak  of  a  mag- 
netic fluid  or  fluids ;  it  is,  however,  absolutely  certain  that 
magnetism  is  not  a  fluid,  whatever  else  it  may  be.  The 
term  is  a  relic  of  bygone  times.  A  magnet  when  rubbed 
upon  a  piece  of  steel  magnetizes  it  without  giving  up  or 
losing  any  of  its  own  magnetism.  A  fluid  cannot  possibly 
propagate  itself  indefinitely  without  loss.  The  arguments 
to  be  derived  from  the  behaviour  of  a  magnet  on  breaking, 
and  from  other  experiments  narrated  in  Lesson  X.,  are 
even  stronger.  No  theory  of  magnetism  will  therefore 
be  propounded  until  these  facts  have  been  placed  before 
the  student. 


LESSON  IX.  —  Methods  of  making  Magnets 

100.  Magnetization  by  Single  Touch.  —  It  has  been 
so  far  assumed  that  bars  or  needles  of  steel  were  to  be 
magnetized  by  simply  touching  them,  or  stroking  them 
from  end  to  end  with  the  pole  of  a  permanent  magnet  of 
lodestone  or  steel.     In  this  case  the  last  touched  point  of 
the  bar  will  be  a  pole  of  opposite  kind  to  that  used  to  touch 
it ;  and  a  more  certain  effect  is  produced  if  one  pole  of 
the  magnet  be  rubbed  on  one  end  of  the  steel  needle,  and 
the  other  pole  upon  the  other  end.     There  are,  however, 
better  ways  of  magnetizing  a  bar  or  needle. 

101.  Magnetization    by    Divided     Touch.  —  In     this 
method  the   bar  to   be   magnetized   is  laid  down  hori- 


100  ELECTRICITY  AND   MAGNETISM        PART  i 

zontally  ;  two  bar  magnets  are  then  placed  down  upon 
it,  their  opposite  poles  being  together.     They  are  then 
drawn  asunder  from  the  middle  of  the  bar  towards  its 
ends,  and  back,  several  times. 
The  bar  is  then  turned  over, 
and  the   operation   repeated, 
taking  care  to  leave  off  at  the 
Fig.  61.  middle    (see   Fig.   61).     The 

process   is   more    effectual  if 

the  ends  of  the  bar  are  meantime  supported  on  the  poles 
of  other  bar  magnets,  the  poles  being  of  the  same  names 
as  those  of  the  two  magnets  above  them  used  for  strok- 
ing the  steel  bar. 

102.  Magnetization     by    Double     Touch.  —  Another 
method,  known  as  double  touch,  differs  slightly  from  that 
last  described.     A  piece  of  wood  or  cork  is  interposed 
between  the  ends  of  the  two  bar  magnets  employed,  and 
they  are  then  both  moved  backwards  and  forwards  along 
the   bar  that  is  to  be  magnetized.     By  none  of  these 
methods,  however,  can  a  steel  bar  be  magnetized  beyond 
a  certain  degree  of  intensity. 

103.  Forms  of  Magnets.  —  Natural  magnets  are  usu- 
ally of  irregular  form,  though  they  are  sometimes  reduced 
to  regular  shapes  by  cutting  or  grinding.     Formerly  it 
was  the  fashion  to  mount  them  with  soft  iron  cheeks  or 
"  armatures  "  to  serve  as  pole-pieces. 

For  scientific  experiments  bar  magnets  of  hardened 
steel  are  commonly  used ;  but  for  many  purposes  the 
horse-shoe  shape  is  preferred.  In  the  horse-shoe  magnet 
the  poles  are  bent  round  so  as  to  approach  one  another, 
the  advantage  here  being  that  so  both  poles  can  attract 
one  piece  of  iron.  The  "  armature,"  or  "  keeper,"  as  the 
piece  of  soft  iron  placed  across  the  poles  is  named,  is 
itself  rendered  a  magnet  by  induction  when  placed  across 
the  poles ;  hence,  when  both  poles  magnetize  it,  the  force 
with  which  it  is  attracted  to  the  magnet -is  the  greater. 

104.  Laminated  Magnets.  —  It  is  found  that  long 


CHAP,  ii  LAMINATED   MAGNETS  101 

thin  steel  magnets  are  more  powerful  in  proportion  to 
their  weight  than  thicker  ones.  Hence  it  was  proposed 
by  Scoresby*  to  construct  compound  magnets,  consisting 
of  thin  laminae  of  steel  separately  magnetized,  and  after- 


Fig.  62.  Fig.  63. 

wards  bound  together  in  bundles  (Fig.  62).  These 
laminated  magnets  are  more  powerful  than  simple  bars 
of  steel.  Compound  horse-shoe  magnets  are  sometimes 
used :  the  plates  separately  magnetized  are  assembled  as 
in  Fig.  63. 

105.  Magnetization  derived  from  the  Earth.  —  The 
magnetism  of  the  earth  may  be  utilized  where  no  other 
permanent  magnet  is  available  to  magnetize  a  bar  of 
steel.      Gilbert  states  that  iron  bars  set   upright  for  a 
long  time  acquire  magnetism  from  the  earth.     If  a  steel 
poker  be  held  in  the  magnetic  meridian,  with  the  north 
end  dipping  down,  and  in  this  position  be  struck  with 
a  wooden    mallet,   it  will   be   found  to   have   acquired 
magnetic  properties.     All  vertical  iron  columns  in   our 
northern  latitudes  are  found  to  have  their  lower  ends 
N  poles  and  their  upper  ends  S  poles.     In  Australia  and 
the  southern  hemisphere  the  tops  of  iron  columns  are 
N"  poles.     Wires  of  steel  subjected  to  torsion,  while  in 
the  magnetic  meridian,  are  also   found   to    be   thereby 
magnetized. 

106.  Magnetization  after  Heating.  —  Gilbert  discov- 
ered also  that  if  a  bar  of  steel  be  heated  to  redness,  and 
cooled,  either  slowly   or  suddenly,  while  lying  in   the 
magnetic  meridian,  it  acquires  magnetic   polarity.     No 

*  A  similar  suggestion  was  made  by  Geuns  of  Venlo  in  1768,  using 
horse-shoe  magnets.  Similar  magnets  have  been  constructed  in  recent 
years  by  Jainin. 


102  ELECTRICITY  AND   MAGNETISM        PART  i 

such  property  is  acquired  if  it  is  cooled  while  lying  east 
and  west.  It  has  been  proposed  to  make  powerful  mag- 
nets by  placing  hot  bars  of  steel  to  cool  between  the 
poles  of  very  powerful  electromagnets;  and  Carre  pro- 
duced strong  magnets  of  iron  cast  in  moulds  lying  in  an 
intense  magnetic  field. 

107.  Magnetization  by  Currents  of  Electricity.  —  A 
current  of  electricity  caused  to  circulate  in  a  spiral  wire 
wound  around  a  core  of  iron  or  steel  magnetizes  it  more 
powerfully  than   in    any  of   the   preceding   operations. 

In  the  case  of  a  soft  iron  core,  it  is 
only  a  magnet  while  the  current  con- 
tinues to  flow.  Such  a  combination  is 
termed  an  Electromagnet;  it  is  fully 
described  in  Lesson  XXXI.  Fig.  64 
depicts  a  common  form  of  electro- 
magnet having  two  coils  of  insulated 
copper  wire  wound  upon  bobbins  that 
Fig.  64.  are  placed  upon  the  limbs  of  a  soft 

iron  core.  The  armature  is  also  of 
soft  iron  of  sufficient  thickness.  Steel  bars  may  be  mag- 
netized by  drawing  them  over  the  poles  of  such  an 
electromagnet  while  the  latter  is  excited  by  the  circula- 
tion of  the  electric  current.  Elias  of  Haarlem  proposed 
to  magnetize  steel  bars  by  passing  them  through  a  wire 
coiled  up  into  a  compact  ring  of  many  turns,  through 
which  a  strong  current  was  sent  by  a  voltaic  battery. 

108.  Hardening  and   Tempering   of   Steel  for  Mag- 
nets.—  There  are  two  ways  of  hardening  steel:  (1)  by 
suddenly    cooling   it   from    a   bright   red   temperature; 
(2)  by  compressing  it  under  hydraulic  pressure  while  it 
cools  slowly.     If  rods  of  steel  are  heated  brilliantly  red, 
and  then  quenched  in  water,  oil,  or  mercury,  they  become 
intensely  brittle  and  glass-hard.     To  temper  hard  steel 
it  is  then  gently  reheated  to  near  a  very  dull  red  heat 
and  softens  slightly  while  acquiring  a  straw  tint.     If  let 
down  still  further  by  continuing  the  reheating  it  becomes 


CHAP,  ii  UNVARYING  MAGNETS  103 

a  blue  tint,  and  is  springy  and  flexible.  Short  bar  mag- 
nets retain  most  magnetism  if  left  glass-hard  without 
tempering.  But  magnets  whose  length  is  more  than 
twenty  times  their  thickness  retain  more  magnetism  if 
tempered  down  to  a  straw  or  even  to  a  blue  tint. 

109.  Destruction  of  Magnetism.  —  A  steel  magnet  loses 
its  magnetism  partially  or  wholly  if  subjected  to  rough 
usage,  or  if  purposely  hit  or  knocked  about.  Newly  mag- 
netized magnets  lose  more  strength  by  rough  treatment 
than  those  which  have  been  long  magnetized.  A  magnet 
loses  its  magnetism,  as  Gilbert  showed,  on  being  raised 
to  a  bright  red-heat.  The  slightest  vibration  will  de- 
stroy any  magnetism  remaining  in  annealed  soft  iron. 

HO.  Magnets  of  Unvarying  Strength,  —  Ordinary  steel 
magnets  have  by  no  means  a  permanent  or  constant  mag- 
netism. They  soon  lose  a  considerable  percentage  of 
their  magnetism,  and  the  decay  continues  slowly  for 
months  and  years.  Every  shock  or  jolt  to  which  they 
are  subjected,  every  contact  with  iron,  every  change  of 
temperature  weakens  them.  Every  time  that  the  keeper 
is  slammed  on  to  a  horse-shoe  magnet  it  is  weakened. 
For  the  purpose  of  making  magnetic  measurements,  and 
for  use  as  controlling  magnets  of  galvanometers,  magnets 
are,  however,  required  that  shall  possess  the  utmost  con- 
stancy in  their  strength.  Magnets  of  unvarying  strength 
may  be  made  by  attention  to  following  points.  Choose 
a  form  either  of  a  nearly  closed  circuit  or  of  a  very  long 
rod.  Let  the  steel  be  hardened  as  much  as  possible  (see 
Art.  108  above),  then  placed  in  steam  at  100°  for  twenty 
or  thirty  hours  or  more.  Then  magnetize  as  fully  as 
possible,  and  then  heat  again  for  five  hours  in  steam. 
Magnets  of  a  shape  constituting  a  nearly  closed  circuit 
are  more  constant  than  short  straight  magnets. 

111.  Effects  of  Heat  on  Magnetization. — If  a  perma- 
nent steel  magnet  be  warmed  by  placing  it  in  hot  or  boil- 
ing water,  its  strength  will  be  thereby  lessened,  though 
it  recovers  partially  on  cooling.  Chilling  a  magnet  in- 


104  ELECTRICITY  AND   MAGNETISM        PART  i 

creases  its  strength.  Cast  iron  ceases  to  be  attracted  by 
a  magnet  at  a  bright  red-heat,  or  at  a  temperature  of 
about  700°  C.  Cobalt  retains  its  magnetism  at  the  high- 
est temperatures.  Chromium  ceases  to  be  magnetic  at 
about  500°  C.,  and  nickel  at  350°  C.  Manganese  ex- 
hibits magnetic  attraction  only  when  cooled  to  —  20°  C. 
It  has  therefore  been  surmised  that  other  metals  would 
also  become  magnetic  if  cooled  to  a  low  enough  tempera- 
ture. Trowbridge  found  severe  cooling  to  100°  below 
zero  to  destroy  the  magnetism  of  steel  magnets;  but 
Dewar  has  observed  that  when  cooled  to  near  —  200°  C. 
in  liquid  oxygen  the  magnetic  properties  of  iron  are 
nearly  twice  as  high  as  at  0°  C.  The  magnetic  metals  at 
high  temperatures  do  not  become  diarnagnetic,  but  are 
still  feebly  magnetic. 

112.  Magnetic  Saturation. —  A  magnet  to  which  as 
powerful  a  degree  of  magnetization  as  it  can  attain  to  has 
been  given  is  said  to  be  saturated.     A  recently  magnetized 
magnet  will  occasionally  appear  to  be  super-saturated,  pos- 
sessing even  after  the  application  of  the  magnetizing  force 
has  ceased  a  higher  degree  of  magnetism  than  it  is  able 
to  retain  permanently.     Thus  a  horse-shoe-shaped  steel 
magnet  will  support  a  greater  weight  immediately  after 
being  magnetized  than  it  will  do  after  its  armature  has 
been  once  removed  from  its  poles.     Even  soft  iron  after 
being  magnetized  retains  a  small  amount  of  magnetism 
when  its   temporary  magnetism   has   disappeared.      This 
small  remaining  magnetic  charge  is  spoken  of  as  residual 
magnetism. 

113.  Strength  of  a  Magnet.  —  The  "strength"  of  a 
magnet  is  not  the  same  thing  as  its  "  lifting  power."     Its 
lifting  power  is  a  very  uncertain  quantity  depending  not 
only  on  the  shape  of  its  polar  surfaces,  but  on  the  shape 
and  quality  of  the  mass  of  iron  used  as  load.     Conse- 
quently the  "  strength  "  of  a  magnet  pole  must  be  meas- 
ured by  the  magnetic  force  which  it  exerts  at  a  distance 
on  other  magnets.     Thus,  suppose  there  are  two  magnets, 


CHAP,  ii  LIFTING   POWER  105 

A  and  B,  whose  strengths  we  compare  by  making  them 
each  act  upon  the  N  pole  of  a  third  magnet  C.  If  the  N 
pole  of  A  repels  C  with  twice  as  much  force  as  that  with 
which  the  N  pole  of  B  placed  at  the  same  distance  would 
repel  C,  then  we  should  say  that  the  "  strength  "  of  A  was 
twice  that  of  B.  Another  way  of  putting  the  matter  is 
to  say  that  the  "  strength  "  of  a  pole  is  the  amount  of  free 
magnetism  at  that  pole.  By  adopting  the  unit  of  strength 
of  magnet  poles  as  defined  in  Art.  141,  we  can  express 
the  strength  of  any  pole  in  numbers  as  so  many  "  units  " 
of  strength. 

114.  Lifting  Power.  —  The  lifting  power  of  a  magnet 
(also  called  its  portative  force}  depends  both  upon  the 
form  of  the  magnet  and  on  its  magnetic  strength.  A 
horse-shoe  magnet  will  lift  a  load  three  or  four  times  as 
great  as  a  bar  magnet  of  the  same  weight  will  lift.  A 
long  bar  magnet  will  lift  more  than  a  short  bar  magnet 
of  equal  strength.  A  bar  magnet  with  a  rounded  or 
chamfered  end  will  lift  more  than  a  similar  bar  with  a 
flat  or  expanded  end,  though  both  may  be  equally 
strongly  magnetized.  Also  the  lifting  power  of  a  mag- 
net grows  in  a  very  curious  and  unexplained  way  by 
gradually  increasing  the  load  on  its  armature  day  by 
day  until  it  bears  a  load  which  at  the  outset  it  could  not 
have  done.  Nevertheless,  if  the  load  is  so  increased  that 
the  armature  is  torn  off,  the  power  of  the  magnet  falls 
at  once  to  its  original  value.  The  attraction  between  a 
powerful  electromagnet  and  its  armature  may  amount  to 
200  Ibs.  per  square  inch,  or  14,000  grammes  per  square 
centimetre  (see  Art.  384).  Small  magnets  lift  a  greater 
load  in  proportion  to  their  own  weight  than  large  ones,* 
because  the  lifting  power  is  proportional  to  the  polar 

*  Bernoulli  gave  the  following  rule  for  finding  the  lifting  power  p  of 
a  magnet  whose  weight  was  w  :  — 


p  = 

where  a  is  a  constant  depending  on  the  goodness  of  the  steel  and  the 


106  ELECTRICITY  AND   MAGNETISM       PART  I 

surface,  other  things  being  equal.  Steel  magnets  sel- 
dom attain  a  tractive  force  as  great  as  40  Ibs.  per  square 
inch  of  polar  surface.  A  good  steel  horse-shoe  magnet 
weighing  itself  1  Ib.  ought  to  lift  25  Ibs.  weight.  Sir 
Isaac  Newton  is  said  to  have  possessed  a  little  lodestone 
mounted  in  a  signet  ring  which  would  lift  a  piece  of  iron 
200  times  its  own  weight. 


LESSON  X.  —  Distribution  of  Magnetism 

115.  Magnetic  Field.  —  The  space  all  round  a  magnet 
pervaded  by  the  magnetic  forces  is  termed  the  "field"  of  that 
magnet.  It  is  most  intense  near  the  poles  of  the  magnet, 
and  is  weaker  and  weaker  at  greater  distances  away.  At 
every  point  in  a  magnetic  field  the  force  has  a  particular 
strength,  and  acts  in  a  particular  direction.  It  is  pos- 
sible at  any  point  in  a  magnetic  field  to  draw  a  line  in 
the  direction  of  the  resultant  magnetic  force  acting  at  that 
point.  The  whole  field  may  in  this  way  be  mapped  out 
with  magnetic  lines  (Art.  119).  For  a  horse-shoe  magnet 
the  field  is  most  intense  between  the  two  poles,  and  the 
lines  of  magnetic  force  are  curves  which  pass  from 
one  pole  to  the  other  across  the  field.  A  practical  way 
of  investigating  the  distribution  of  the  magnetic  lines 
in  a  field  is  given  in  Art.  119,  under  the  title  "  Mag- 
netic Figures."  When  the  armature  is  placed  upon  the 
poles  of  a  horse-shoe  magnet,  the  force  of  the  magnet  on 
all  the  external  regions  is  weakened,  for  the  induction 
now  goes  on  through  the  iron  of  the  keeper,  not  through 
the  surrounding  space.  In  fact  a  closed  system  of  magnets 
—  such  as  that  made  by  placing  four  bar  magnets  along 
the  sides  of  a  square,  the  N  pole  of  one  touching  the  S 

method  of  magnetizing  it.  In  the  best  steel  magnets  made  at  Haarlem 
by  Van  Wetteren  this  coefficient  was  from  19 '5  to  23,  the  weights  being  ex- 
pressed in  kilogrammes. 


CHAP.    II 


BREAKING  A  MAGNET 


107 


pole  of  the  next  —  has  no  external  field  of  force.  A  ring 
of  steel  may  thus  be  magnetized  so  as  to  have  neither 
external  field  nor  poles ;  or  rather  any  point  in  it  may 
be  regarded  as  a  N  pole  and  a  S  pole,  so  close  together 
that  they  neutralize  one  another's  forces. 

That  poles  of  opposite  name  do  neutralize  one  another 
may  be  shown  by  the  well-known  experiment  of  hanging 
a  small  object  —  a  steel  ring  or  a  key  —  to  the  N  pole  of 
a  bar  magnet.  If  now  the  S  pole  of  another  bar  magnet 
be  made  to  touch  the  first  the  two  poles  will  neutralize 
each  other's  actions,  and  the  ring  or  key  will  drop  down. 

116.  Breaking  a  Magnet. — We  have  already  stated 
that  when  a  magnet  is  broken  into  two  or  more  parts, 
each  is  a  complete  magnet,  possessing  poles,  and  each  is 
nearly  as  strongly  magnetized  as  the  original  magnet. 


Fig.  65. 

Fig.  65  shows  this.  If  the  broken  parts  be  closely  joined 
these  adjacent  poles  neutralize  one  another  and  disappear, 
leaving  only  the  poles  at  the  ends  as  before.  If  a  magnet 
be  ground  to  powder  each  fragment  will  still  act  as  a 


N 


S'N' 


n         .v 

n        .s 

n       x 

•n      N 

It         N 

n       s 

71          .S 

n       s 

n        .s' 

n       s 

>l        .s 

«      s 

n      .<? 

"       s 

n      s 

n      s 

n        .<? 

n       K 

n      s 

'?      s 

n       5 

H        S 

n      s 

)l        S 

/  I.           .*; 

n        s 

n      .s 

ll       X 

w       s 

n      s 

n      s 

n      s 

N                                S'N'                              S 

Fig.  66. 

little  magnet  and  exhibit  polarity.  A  magnet  may  there- 
fore be  regarded  as  composed  of  many  little  magnets  put 
together,  so  that  their  like  poles  all  face  one  way.  Such 
an  arrangement  is  indicated  in  Fig.  66,  from  which  it 
will  be  seen  that  if  the  magnet  be  broken  asunder  across 


108  ELECTRICITY   AND   MAGNETISM        PART  i 

any  part,  one  face  of  the  fracture  will  present  only  N 
poles,  the  other  only  S  poles.  This  would  be  true  no 
matter  how  small  the  individual  particles. 

117.  Normal  Distribution.  —  In  an  ordinary  bar  mag- 
net the  poles  are  not  quite  at  the  ends  of  the  bar,  but 
a  little  way  from  it ;   and  it  can  be  shown  that  this  is 
a  result  of  the  way  in  which  the  surface  magnetism  is 
distributed  in  the  bar.     A  very  long,  thin,  uniformly 
magnetized  bar  has  its  poles  at  the  ends ;  but  in  ordinary 
thick  magnets  the  "  pole  "  occupies  a  considerable  region, 
the  "free  magnetism"  falling  off  gradually  from  the 
ends  of  the  bar.     In  each  region,  however,  a  point  can 
be  generally  determined  at  which  the  resultant  magnetic 
forces  act,  and  which  may  for  most  purposes  be  considered 
as  the  "  pole."     In  certain  cases  of  irregular  magnetiza- 
tion it  is  possible  to  have  one  or  more   poles  between 
those  at  the  ends.     Such  poles  are  called  consequent  poles 
(see  Fig.  70). 

118.  Lamellar  Distribution  of  Magnetism.     Magnetic 
Shells. — Up  to  this  point  the  ordinary  distribution  of 
magnetism  along  a  bar  has  been  the  only  distribution 
considered.     It  is  theoretically  possible  to  have  magnet- 
ism distributed  over  a  thin  sheet  so  that  the  whole  of 
one  face  of  the  sheet  shall  have  one  kind  of  magnetism, 
and  the  other  face  the  other  kind  of  magnetism;  such 
distribution  is,  however,  unstable.      If  an  immense  num- 
ber of  little  magnets  were  placed  together  side  by  side, 
like  the  cells  in  a  honeycomb,  all  with  their  N-seeking 
ends  upwards,  and  S-seeking  ends  downwards,  the  whole 
of  one  face  of  the  slab  would  be  one  large  flat  N-seeking 
pole,  and  the  other  face  S-seeking.     Such  a  distribution 
as  this  over  a  surface  or  sheet  is  termed  a  lamellar  dis- 
tribution, to  distinguish  it  from  the    ordinary  distribu- 
tion along  a  line  or  bar,  which  is  termed,  for  distinction, 
the   solenoidal,  or  circuital,  distribution.      A   lamellarly 
magnetized  magnet  is  sometimes  spoken  of  as  a  magnetic 
shell. 


CHAP.    II 


MAGNETIC   FIGURES 


109 


119.  Magnetic  Figures.  —  Gilbert  showed*  that  if  a 
sheet  of  paper  or  card  be  placed  over  a  magnet,  and  iron 
filings  are  dusted  over  the  paper,  they  settle  down  in 
curving  lines,  forming  a  magnetic  figure,  the  general  form 
of  which  for  a  bar  magnet  is  shown  in  Fig.  67.  The 
filings  should  be  fine,  and  sifted  through  a  bit  of  muslin  ; 
to  facilitate  their  settling  in  the  lines,  the  sheet  of  paper 
should  be  lightly  tapped.  The  figures  thus  obtained  can 
be  fixed  permanently  by  several  processes.  The  best  of 
these  consists  in  employing  a  sheet  of  glass  which  has 


Fig.  6T. 

been  previously  gummed  arid  dried,  instead  of  the  sheet 
of  paper;  after  this  has  been  placed  above  the  magnet 
the  filings  are  sifted  evenly  over  the  surface,  and  then 
the  glass  is  tapped  ;  then  a  jet  of  steam  is  caused  to  play 
gently  above  the  sheet,  softening  the  surface  of  the  gum, 
which,  as  it  hardens,  fixes  the  filings  in  their  places.  In- 
spection of  the  figure  will  show  that  the  lines  diverge 
nearly  radially  from  each  pole,  and  curve  round  to  meet 
these  from  the  opposite  pole.  Fig.  68,  produced  from  a 
horse-shoe  magnet,  shows  how  the  magnetic  field  is  most 

*  The  magnetic  figures  were  known  to  Lucretius. 


110 


ELECTRICITY   AND   MAGNETISM        PART  i 


intense  between  the  poles,  but  spreads  beyond  them  in 
wide  curves.     Faraday,  who  made  a  great  use  of  this 

method  of  investigating 
the  distribution  of  mag- 
netism in  various  "  fields," 
gave  to  the  lines  the  name 
of  lines  of  force.  They 
represent,  as  shown  by  the 
action  on  little  magnetic 
particles  which  set  them- 
selves thus  in  obedience  to 
the  attractions  and  repul- 
sions in  the  field,  the  re- 
sultant direction  of  the 
forces  at  every  point ;  for 
each  particle  tends  to  as- 
sume the  direction  of  the 
force  jointly  due  to  the 
simultaneous  action  of 


Fig.  65 


both  poles ;  hence  the  curves  of  filings  may  be  taken  to 
represent  visibly  the  in- 
visible lines  of  magnetic 
force.*  Faraday  pointed  out 
that  these  "  lines  of  force  " 
map  out  the  magnetic  field, 
showing  by  their  position  the 
direction  of  the  magnetic 
force,  and  by  their  number 
its  intensity.  If  a  small  N- 
seeking  pole  could  be  obtained 
alone,  and  put  down  on  any 
one  of  these  lines  of  force,  it  Fig.  69 

would  tend   to    move   along 
that  line  from  N  to  S;   a  single  S-seeking  pole  would 

*  Or  rather  the  component  part  of  the  magnetic  force  resolved  into  the 
plane  of  the  figure  ;  which  is  not  quite  the  same  thing,  for  above  the  poles 
the  filings  stand  up  nearly  vertically  to  this  plane. 


CHAP,  ii  CONSEQUENT  POLES  111 

tend  to  move  along  the  line  in  an  opposite  direction.  In 
Fig.  69,  which  is  the  field  about  one  end  of  a  bar  magnet, 
the  magnetic  lines  are  simply  radial.  Faraday  also 
pointed  out  that  the  actions  of  attraction  or  repulsion 
in  the  field  are  always  related  to  the  directions  in  the 
field  of  the  magnetic  lines.  He  assigned  to  these  lines  of 
force  certain  physical  properties  (which  are,  however,  only 
true  of  them  in  a  secondary  sense),  viz.  that  they  tend  to 
shorten  themselves  from  end  to  end,  and  that  they  repel 
one  another  as  they  lie  side  by  side.  The  modern  way 
of  stating  the  matter  is,  that  in  every  magnetic  field 
there  are  certain  stresses,  consisting  of  a  tension  along 
the  lines  of  force,  and  a  pressure  across  them. 

12O.    Consequent  Poles.  —  The  method  of  sprinkling 
filings  may  be  applied  to  ascertain  the  presence  of  conse- 


Fig.  70. 

quent  poles  in  a  bar  of  steel,  the  figure  obtained  resem- 
bling that  depicted  in  Fig.  70.  Such  a  state  of  things  is 
produced  when  a  strip  of  very  hard  steel  is  purposely 
irregularly  magnetized  by  touching  it  with  strong  mag- 
nets at  certain  points.  A  strip  thus  magnetized  virtually 
consists  of  several  magnets  put  end  to  end,  but  in  reverse 
directions,  NS,  SN,  etc.  Consequent  poles  can  also  be 
produced  in  an  electromagnet  by  reversing  the  direction 
in  which  the  wire  is  coiled  around  part  of  the  core. 

121.   Fields   mapped    by  Filings.  —  The  forces  pro- 


112  ELECTRICITY  AND   MAGNETISM        PART  i 

ducing  attraction  between  unlike  poles,  and  repulsion 
between  like  poles,  are  beautifully  illustrated  by  the 
magnetic  figures  obtained  in  the  fields  between  the  poles 
in  the  two  cases,  as  given  in  Figs.  71  and  72.  In  Fig.  71 
the  poles  are  of  opposite  kinds,  and  the  lines  of  force 
curve  across  out  of  one  pole  into  the  other ;  while  in  Fig. 


Fig.  71.  Fig.  72. 

72,  which  represents  the  action  of  two  similar  poles,  the 
lines  of  force  curve  away  as  if  repelling  one  another,  and 
turn  aside  at  right  angles. 

122.  Magnetic    Writing.  —  Another   kind   of    mag- 
netic figures  was  discovered  by  De  Haldat,  who  wrote 
with  the  pole  of  a  magnet  upon  a  thin  steel  plate  (such 
as  a  saw-blade),  and  then  sprinkled  filings  over  it.     The 
writing,  which  is  quite  invisible  in  itself,  comes  out  in 
the  lines  of  filings  that  stick  to  the  magnetized  parts ; 
this  magic  writing  will  continue  in  a  steel  plate  many 
months. 

123.  Surface    Magnetization.  —  In   many  cases  the 
magnetism  imparted  to  magnets  is  confined  chiefly  to 
the  outer  layers  of  steel.     If  a  short  bar  magnet  be  put 
into  acid  so  that  the  outer  layers  are  dissolved  away,  it 
is  found  that  it  has  lost  its  magnetism  when  only  a  thin 
film  has  been  thus  removed.     A  short  hollow  steel  tube 
when  magnetized  is  nearly  as  strong  a  magnet  as  a  solid 
rod  of  the  same  size.     Long  thin  magnets,  and  those  that 
are  curved  so  as  nearly  to  form  a  closed  circuit  can  be 
much  more  thoroughly  magnetized.     If  a  bundle  of  steel 
plates  are  magnetized  while  bound   together,  it  will  be 


CHAP.  11       EFFECTS   OF   MAGNETIZATION  113 

found  that  only  the  outer  ones  are  strongly  magnetized. 
The  inner  ones  may  even  exhibit  a  reversed  magnetization. 

124.  Mechanical  Effects   of    Magnetization.  —  Joule 
found  an  iron  bar  to  increase  by  72oW^  of  its  length 
when  strongly   magnetized.     Bidwell  found  that  with 
still  stronger  magnetizing  forces  iron  contracts  again ; 
and  rods  stretched  by   a  weight  contract  more  when 
magnetized  than  unstretched  rods  do.     Barrett  observed 
that  nickel  shows  a  slight  contraction  when  magnetized. 
These  are  proofs  that  magnetization  is  an  action  affecting 
the  arrangement  of  the  molecules.     This  supposition  is 
confirmed  by  the  observation  of  Page,  that  at  the  moment 
when  a  bar  is  magnetized  or  demagnetized,  a  faint  metal- 
lic clink  is  heard  in  the  bar.     Sir  W.  Grove  showed  that 
when  a  tube  containing  water  rendered  muddy  by  stir- 
ring up  in  it  finely  divided  magnetic  oxide  of  iron  was 
magnetized,  the  liquid  became  clearer  in  the  direction  of 
magnetization,  the  particles  apparently  setting  themselves 
end-on,  and  allowing  more  light  to  pass  between  them. 
A  twisted  iron  wire  tends  to  untwist  itself  when  magnet- 
ized.    A  piece  of  iron,  when  powerfully  magnetized  and 
demagnetized  in  rapid  succession,  grows  hot,  as  if  mag- 
netization were  accompanied  by  internal  friction. 

125.  Action    of    Magnetism    on    Light.  —  Faraday 
discovered  that  a  ray  of  polarized  light  passing  through 
certain  substances  in  a  powerful  magnetic  field  has  the 
direction  of  its  vibrations  changed.     This  phenomenon, 
which  is  sometimes  called  "  The  Magnetization  of  Light," 
is  better  described  as  "The   Rotation  of  the   Plane  of 
Polarization  of  Light  by  Magnetism."     The  amount  of 
rotation  differs  in  different  media,  and  varies  with  the 
magnetizing  force.     More  recently  Kerr  has  shown  that 
a  ray  of  polarized  light  is  also  rotated  by  reflexion  at  the 
end  or  side  of  a  powerful  magnet.     Further  mention  is 
made  of  these  discoveries  in  the  chapter  on  Electro-optics, 
Lesson  LVI. 

126.  The  Act  of   Magnetizing.  —  All  these  various 
i 


114 


ELECTRICITY   AND   MAGNETISM        PART 


Fig.  73. 


phenomena  point  to  a  theory  of  magnetism  very  different 
from  the  old  notion  of  fluids.  It  appears  that  every 
particle  of  a  magnet  is  itself  a  magnet,  and  that  the 
magnet  only  becomes  a  magnet  as  a  whole  by  the  parti- 
cles being  so  turned  as  to  point  one  way.  The  act  of 
magnetizing  consists  in  turning  the  molecules  more  or  less 
into  one  particular  direction.  This  conclusion  is  supported 
by  the  observation  that  if  a 
glass  tube  full  of  iron  filings 
is  magnetized,  the  filings  can 
be  seen  to  set  themselves  end- 
ways, and  that,  when  thus 
once  set,  they  act  as  a  mag- 
net until  shaken  up.  It  appears  to  be  harder  to  turn 
the  individual  molecules  of  solid  steel  than  those  of 
soft  iron ;  but,  when  once  so  set,  they  remain  end-on 
unless  violently  struck  or  heated.  As  Weber,  who  pro- 
pounded this  notion  of  molecular  magnetism,  pointed 
out,  it  follows  from  this  theory  that  when  all  the  particles 
are  turned  end-on  the  limits  of  possible  magnetization 
would  have  been 

attained.  Some  \  \  \  \  \  /- — -•;  /  /  //  / 
careful  experi- 
ments of  Beetz 
on  iron  deposited 
by  electrolysis 
entirely  confirm 
this  conclusion, 
and  add  weight 
to  the  theory.  Fig.  73  may  be  taken  to  represent  a  non- 
magnetized  piece  of  iron  or  steel  in  which  the  arrangement 
of  the  particles  is  absolutely  miscellaneous :  they  do  not 
point  in  any  one  direction  more  than  another.  When 
magnetized  slightly,  there  will  be  a  greater  percentage 
pointing  in  the  direction  of  the  magnetizing  force.  When 
fully  magnetized  —  if  that  were  possible  —  they  would  all 
point  in  the  same  direction  as  in  Fig.  74. 


Fig.  74. 


CHAP,  ii      THEORY   OF   MAGNETIZATION  115 

In  very  few  cases,  however,  is  the  magnetization 
uniform  throughout  the  whole  length  of  a  bar:  the 
particles  are  more  fully  completely  turned  into  line  at 
the  middle  part  of  the  bar  than  at  the  ends. 

If  the  intrinsic  magnetization  of  the  steel  at  every 
part  of  a  magnet  were  equal,  the  free  poles  would  be 
found  only  at  the  end  surfaces ;  but  the  fact  that  the  free 
magnetism  is  not  at  the  ends  merely,  but  diminishes  from 
the  ends  towards  the  middle,  shows  that  the  intensity  of 
the  intrinsic  magnetization  must  be  less  towards  and 
at  the  ends  than  it  is  at  the  middle  of  the  bar.  In  Fig. 
74  an  attempt  is  made  to  depict  this.  It  will  be  noticed 
that  the  magnetic  lines  run  through  the  steel  and  emerge 
into  the  air  in  curves.  Some  of  the  lines  do  not  run  all 
the  length  of  the  bar  but  leak  out  at  the  sides.  If  the 
bar  were  uniformly  magnetized  the  lines  would  emerge 
at  the  ends  only.  It  is  clear  that  the  middle  piece  is 
more  thoroughly  magnetized  than  any  other  part.  Mag- 
netism in  fact  consists  of  a  sort  of  grain  or  structure  con- 
ferred upon  the  steel.  Wherever  this  structure  comes  up 
at  a  surface,  there  the  surface  properties  of  magnetism  are 
found.  A  pole  is  simply  a  region  where  the  magnetic 
lines  pass  through  the  surface  of  the  steel  or  iron. 

The  optical  phenomena  led  Clerk  Maxwell  to  the 
further  conclusion  that  these  longitudinally-set  molecules 
are  rotating  round  their  long  axes,  and  that  in  the  "  ether  " 
of  space  there  is  also  a  vortical  motion  along  the  lines  of 
magnetic  induction  ;  this  motion,  if  occurring  in  a  perfect 
medium  (as  the  "  ether  "  may  be  considered),  producing 
tensions  along  the  lines  of  the  magnetic  field,  and  press- 
ures at  right  angles  to  them,  would  afford  a  satisfactory 
explanation  of  the  magnetic  attractions  and  repulsions 
which  apparently  act  across  empty  space. 

Hughes,  Barus,  and  others  have  lately  shown  that  the 
magnetism  of  iron  and  steel  is  intimately  connected  with 
the  molecular  rigidity  of  the  material.  Hughes's  re- 
searches with  the  "induction  balance"  (Art.  514)  and 


116  ELECTRICITY   AND   MAGNETISM        PART  i 

"  magnetic  balance  "  (Art.  140)  tended  to  prove  that  each 
molecule  of  a  magnetic  metal  has  an  absolutely  constant 
inherent  magnetic  polarity ;  and  that  when  a  piece  of 
iron  or  steel  is  apparently  neutral,  its  molecules  are  inter- 
nally arranged  so  as  to  satisfy  each  other's  polarity,  form- 
ing closed  magnetic  circuits  amongst  themselves. 

127.  Ewing's  Theory  of  Molecular  Magnetism. — 
Weber  supposed  that  there  was  in  hard  steel  some  sort 
of  friction  which  prevented  the  molecules  when  once 
magnetized  from  turning  back  into  higgledy-piggledy 
positions.  Ewing,  however,  showed  that  a  complete  ex- 
planation was  afforded  by  supposing  the  particles  to  be 
subject  to  mutual  forces.  In  any  group  not  subjected  to 
an  external  magnetizing  force  the  particles  will  arrange 
themselves  so  as  to  satisfy  one  another's  polarity.  Of  the 


Fig.  75. 

possible  groupings  some  are,  however,  unstable.  Four 
possible  stable  groupings  of  six  pivoted  needles  are  shown 
in  Fig.  75.  Ewing  constructed  a  model  consisting  of  a 
large  number  of  pivoted  magnetic  needles  arranged  in 
one  layer.  When  these  needles  were  simply  agitated  and 
allowed  to  come  to  rest  they  settled  down  in  miscellaneous 
groups ;  but  when  acted  upon  by  a  gradually  increasing 
magnetic  force  they  turned  round,  the  operation  showing 
three  stages —  (i.)  with  very  small  magnetizing  force  the 
needles  merely  turned  through  a  small  angle  ;  (ii.)  when 
a  certain  force  was  applied  the  groupings  became  unsta- 
ble, some  of  the  needles  suddenly  swinging  round  to  a  new 
position,  with  the  result  that  the  majority  of  the  needles 


CHAP,  ii        LAWS  OF   MAGNETIC   FORCE  117 

point  nearly  but  not  quite  along  the  direction  of  the 
force ;  (iii.)  a  further  increase  of  the  magnetizing  force 
cannot  produce  much  more  effect;  it  can  only  pull  the 
needles  a  little  more  perfectly  into  line.  All  these  things 
correspond  to  the  three  stages  observed  (see  Art.  364)  in 
the  gradual  magnetization  of  iron  or  steel. 


LESSON  XI.  —  Laws  of  Magnetic  Force 

128.  Laws  of  Magnetic  Force. 

FIRST  LAW.  —  Like  magnetic  poles  repel  one 
another;  unlike  magnetic  poles  attract  one 
another. 

SECOND  LAW.  —  The  force  exerted  between  two 
magnetic  poles  is  proportional  to  the  product 
of  their  strengths,  and  is  inversely  propor- 
tional to  the  square  of  the  distance  between 
them,  provided  that  the  distance  is  so  great 
that  the  poles  may  be  regarded  as  mere  points. 

129.  The   Law  of   Inverse    Squares. — The    second 
of  the  above  laws  is  commonly  known   as  the   law  of 
inverse  squares;   it 

is  essentially  a  law 
of  point -action, 
and  is  not  true  for 
poles  of  elongated 
or  extended  sur- 
face. The  similar 
law  of  electrical 
attraction  has  al- 
ready  been  explained  and  illustrated  (Art.  19).  This  law 
furnishes  the  explanation  of  a  fact  mentioned  in  an  earlier 
lesson,  Art.  91,  that  small  pieces  of  iron  are  drawn  bodily 
up  to  a  magnet  pole.  If  a  small  piece  of  iron  wire,  a,  b  (Fig. 
76),  be  suspended  by  a  thread,  and  the  N-poiuting  pole 


118  ELECTRICITY  AND   MAGNETISM        PART  i 

A  of  a  magnet  be  brought  near  it,  the  iron  is  thereby  in- 
ductively magnetized ;  it  turns  round  and  points  towards 
the  magnet  pole,  setting  itself  as  nearly  as  possible 
along  a  line  of  force,  its  near  end  b  becoming  a  S-seeking 
pole,  and  its  farther  end  a  becoming  a  N-seeking  pole. 
Now  the  pole  b  will  be  attracted  and  the  pole  a  will  be 
repelled.  But  these  two  forces  do  not  exactly  equal  one 
another,  since  the  distances  are  unequal.  The  repulsion 
will  (by  the  law  of  inverse  squares)  be  proportional  to 

- — — ;  and  the  attraction  will  be  proportional  to  ,  .  .     • 
(Aa)2  (A&)2 

Hence  the  bit  of  iron  a,  b  will  experience  a  pair  of  forces, 
turning  it  into  a  certain  direction,  and  also  a  total  force 
drawing  it  bodily  toward  A.  Only  those  bodies  are 
attracted  by  magnets  in  which  magnetism  can  thus  be 
induced;  and  they  are  attracted  only  because  of  the 
magnetism  induced  in  them. 

We  mentioned,  Art.  91,  that  a  magnet  needle  floating 
freely  on  a  bit  of  cork  on  the  surface  of  a  liquid,  is  acted 
upon  by  forces  that  give  it  a  certain  direction,  but  that, 
unlike  the  last  case,  it  does  not  tend  to  rush  as  a  whole 
either  to  the  north  or  to  the  south.  It  experiences  a 
rotation,  because  the  attraction  and  repulsion  of  the 
magnetic  poles  of  the  earth  act  in  a  certain  direction; 
but  since  the  magnetic  poles  of  the  earth  are  at  a  distance 
enormously  great  as  compared  with  the  length  from  one 
pole  of  the  floating  magnet  to  the  other,  we  may  say  that, 
for  all  practical  purposes,  the  poles  of  the  magnet  are  at 
the  same  distance  from  the  N  pole  of  the  earth.  The 
attracting  force  on  the  N-pointing  pole  of  the  needle  is 
therefore  practically  no  greater  than  the  repelling  force 
acting  on  the  S-pointing  pole,  hence  there  is  no  motion 
of  translation  given  to  the  floating  needle  as  a  whole :  it 
is  directed,  not  attracted. 

130.  Measurement  of  Magnetic  Forces.  —  The  truth 
of  the  law  of  inverse  squares  can  be  demonstrated  by 
experiment.  But  this  implies  that  we  have  some  means 


CHAP.    II 


MEASUREMENT  OF  FORCE 


110 


of  measuring  accurately  the  amount  of  the  magnetic 
forces  of  attraction  or  repulsion.  Magnetic  force  may  be 
measured  in  any  one  of  the  four  following  ways :  (1)  by 
observing  the  time  of  swing  of  a  magnetic  needle  oscil- 
lating under  the  influence  of  the  force ;  (2)  by  observing 
the  deflexion  it  produces  upon  a  magnetic  needle  which 
is  already  attracted  into  a  different  direction  by  a  force 
of  known  intensity ;  (3)  by  balancing  it  against  the  tor- 
sion of  an  elastic  thread ;  (4)  by  balancing  it  against  the 
force  of  gravity  as  brought  into  play  in  attempting  to 
deflect  a  magnet  hung  by  two  parallel  strings  (called  the 
bifilar  suspension),  for  these  strings  cannot  be  twisted 
out  of  their  parallel  position  without  raising  the  centre 
of  gravity  of  the  magnet. 

131.  Deflexion  Experiment.  —  Fig.  77  shows  an  ap- 
paratus   in    which    a   compass-needle 

can  be  deflected  by  one  pole  of  a 
magnet  made  of  a  long  thin  bar  of 
steel,  so  mounted  that  its  upper  pole 
is  always  over  the  centre  of  the 
needle,  and  therefore  has  no  tendency 
to  turn  it.  So  set,  it  acts  as  a  one- 
pole  magnet,  the  pole  of  which  can 
be  placed  at  different  distances  from 
the  compass-needle.  It  is  found,  using 
a  proper  tangent-scale  (see  Art.  211) 
for  the  compass-needle,  that  when  the 
distance  is  doubled  the  deflecting  force  is  reduced  to  one 
quarter,  and  so  forth. 

132.  The  Torsion   Balance.  —  Coulomb  applied  the 
Torsion  Balance  to  the  measurement  of  magnetic  forces. 
The  main  principles  of  this  instrument  (as  used  to  meas- 
ure forces  of  electrostatic  repulsion)  were  described  on 
p.  20.    Fig.  78  shows  how  it  is  arranged  for  measuring 
magnetic  repulsions. 

To  prove  the  law  of  inverse  squares,  Coulomb  made  the 
following  experiment :  —  The  instrument  was  first  adjusted 


120 


ELECTRICITY   AND   MAGNETISM      PART  i 


so  that  a  magnetic  needle,  hung  in  a  copper  stirrup  to  the 
fine  silver  thread,  lay  in  the  magnetic  meridian  without 
the  wire  being  twisted.  This  was  done  by  first  putting 
in  the  magnet  and  adjusting  roughly,  then  replacing  it  by 
a  copper  bar  of  equal  weight,  and  once  more  adjusting, 
thus  diminishing  the  error  by  repeated  trials.  The  next 


step  was  to  ascertain  through  what  number  of  degrees  the 
torsion-head  at  the  top  of  the  thread  must  be  twisted  in 
order  to  drag  the  needle  1°  out  of  the  magnetic  meridian. 
In  the  particular  experiment  cited  it  was  found  that  35° 
of  torsion  corresponded  to  the  1°  of  deviation  of  the 
magnet ;  then  a  magnet  was  introduced  through  the  lid, 
that  pole  being  downwards  which  repelled  the  pole  of  the 


CHAP,  ii  TORSION  BALANCE  121 

suspended  needle.  It  was  found  (in  this  particular  ex- 
periment) to  repel  the  pole  of  the  needle  through  24°. 
From  the  preliminary  trial  we  know  that  this  directive 
force  corresponds  to  24°  x  35°  of  the  torsion-head,  and  to 
this  we  must  add  the  actual  torsion  on  the  wire,  viz.  the 
24°,  making  a  total  of  864°,  which  we  will  call  the 
"  torsion  equivalent "  of  the  repelling  force  when  the  poles 
are  thus  24°  apart.  Finally  the  torsion-head  was  turned 
round  so  as  to  twist  the  suspended  magnet  round,  and 
force  it  nearer  to  the  fixed  pole,  until  the  distance  between 
the  repelling  poles  was  reduced  to  half  what  it  was  at 
first.  It  was  found  that  the  torsion-head  had  to  be  turned 
round  8  complete  rotations  to  bring  the  poles  to  12°  apart. 
These  8  rotations  were  an  actual  twist  of  8°  x  360°,  or 
2880°.  But  the  bottom  of  the  torsion  thread  was  still 
twisted  12°  as  compared  with  the  top,  the  force  producing 
this  twist  corresponding  to  12  x  35  (or  420°)  of  torsion ; 
and  to  these  the  actual  torsion  of  12°  must  be  added, 
making  a  total  of  2880°  +  420°  +  12°  =  3312.  The 
result  then  of  halving  the  distance  between  the  magnet 
poles  was  to  increase  the  force  fourfold,  for  3312  is  very 
nearly  four  times  864.  Had  the  distance  between  the 
poles  been  reduced  to  one-third  the  force  would  have  been 
nine  times  as  great. 

We  may  also,  assuming  this  law  proved,  employ  the 
balance  to  measure  the  strengths  of  magnet  poles  by 
measuring  the  forces  they  exert  at  known  distances. 

133.  Method  of  Oscillations.*  —  If  a  magnet  sus- 
pended by  a  fine  thread,  or  poised  upon  a  point,  be  pushed 
aside  from  its  position  of  rest,  it  will  vibrate  backwards 
and  forwards,  performing  oscillations  which,  although 
they  gradually  decrease  in  amplitude,  are  executed  in 

*  It  is  possible,  also,  to  measure  electrical  forces  by  a  "  method  of  os- 
cillations "  ;  a  small  charged  ball  at  the  end  of  a  horizontally-suspended  arm 
being  caused  to  oscillate  under  the  attracting  force  of  a  charged  conductor 
near  it,  whose  "  force  "  at  that  distance  is  proportional  to  the  square  of  the 
number  of  oscillations  in  a  given  time. 


122  ELECTRICITY  AND   MAGNETISM        PART  i 

very  nearly  equal  times.  In  fact,  they  follow  a  law  similar 
to  that  of  the  oscillations  executed  by  a  pendulum  swing- 
ing under  the  influence  of  gravity.  The  law  of  pendular 
vibrations  is,  that  the  square  of  the  number  of  oscillations 
executed  in  a  given  time  is  proportional  to  the  force.  Hence 
we  can  measure  magnetic  forces  by  counting  the  oscilla- 
tions made  in  a  minute  by  a  magnet.  It  must  be 
remembered,  however,  that  the  actual  number  of  oscilla- 
tions made  by  any  given  magnet  will  depend  on  the 
weight  of  the  magnet  and  on  its  leverage  around  its 
centre,  as  well  as  upon  the  strength  of  its  poles,  and  on 
the  intensity  of  the  field  in  which  it  may  be  placed  (see 
calculations,  Art.  361). 

We  can  use  this  method  to  compare  the  intensity  of 
the  force  of  the  earth's  magnetism  *  at  any  place  with  that 
at  any  other  place  on  the  earth's  surface,  by  oscillating  a 
magnet  at  one  place  and  then  taking  it  to  the  other  place 
and  oscillating  it  there.  If,  at  the  first,  it  makes  a 
oscillations  in  one  minute,  and  at  the  second  b  oscillations 
a  minute,  then  the  magnetic  forces  at  the  two  places  will 
be  to  one  another  in  the  ratio  of  a2  to  b2. 

Again,  we  may  use  the  method  to  compare  the  force 
exerted  at  any  point  by  a  magnet  near  it  with  the  force 
of  the  earth's  magnetism  at  that  point.  For,  if  we  swing 
a  small  magnetic  needle  there,  and  find  that  it  makes  m 
oscillations  a  minute  under  the  joint  action  f  of  the  earth's 
magnetism,  and  that  of  the  neighbouring  magnet,  and 
that,  when  the  magnet  is  removed,  it  makes  n  oscillations 
a  minute  under  the  influence  of  the  earth's  magnetism 
alone,  then  m2  will  be  proportional  to  the  joint  forces,  n2 
to  the  force  due  to  the  earth's  magnetism,  and  the  differ- 
ence of  these,  or  m2-  n2  will  be  proportional  to  the  force 
due  to  the  neighbouring  magnet. 

*  Or,  more  strictly,  of  its  horizontal  component. 

t  We  are  here  assuming  that  the  magnet  is  so  placed  that  its  force  is  in 
a  line  with  that  of  the  earth's  magnetism  at  the  point,  and  that  the  other 
pole  of  the  magnet  is  so  far  away  as  not  to  affect  the  oscillating  needle. 


CHAP,  ii        DISTRIBUTION   ON   SURFACE  123 

134.  Surface  Distribution.  —  We  will  now  apply  the 
method  of  oscillations  to  measure  the  relative  quantities 
of  surface  magnetism  at  different  points  along  a  bar 
magnet.  The  magnet  to  be  examined  is  set  up  vertically 
(Fig.  79).  A  small  magnet,  capable  of  swinging  hori- 
zontally, is  brought  near  it  and  set  at  a  short  distance 
away  from  its  extremity,  and  then  oscillated,  while  the 
rate  of  its  oscillations  is  counted.  Suppose 
the  needle  were  such  that,  when  exposed 
to  the  earth's  magnetism  alone,  it  would  14— - 
perform  3  complete  oscillations  a  minute, 
and  that,  when  vibrating  at  its  place  near  g  " 
the  end  of  the  vertical  magnet  it  oscillated  6 
14  times  a  minute,  then  the  force  due  5- 
to  the  magnet  will  be  proportional  to  *' 
142  -  32  =  196  -  9  =  187.  Nextly,  let 
the  oscillating  magnet  be  brought  to  an 
equal  distance  opposite  a  point  a  little 
away  from  the  end  of  the  vertical  magnet. 
If,  here,  it  oscillated  12  times  a  minute, 
we  know  that  the  force  will  be  proper- 
tional  to  122  -  32  =  144  -  9  =  135.  So 
we  shall  find  that  as  the  force  falls  off  the  oscillations 
will  be  fewer,  until,  when  we  put  the  oscillating  magnet 
opposite  the  middle  of  the  vertical  magnet,  we  shall  find 
that  the  number  of  oscillations  is  3  per  minute,  or  that 
the  earth's  force  is  the  only  force  affecting  the  oscillations. 
In  Fig.  80  we  have  indicated  the  number  of  oscillations 
at  successive  points,  as  14,  12,  10,  8,  6,  5,  4,  and  3. 
If  we  square  these  numbers  and  subtract  9  from  each, 
we  shall  get  for  the  forces  at  the  various  points  the 
following :  — 187,  135,  91,  55,  27,  16,  7,  and  0.  _  These 
forces  may  be  taken  to  represent  the  strength  of  the  free 
magnetism  at  the  various  points,  and  it  is  convenient  to 
plot  them  out  graphically  in  the  manner  shown  in  Fig.  80, 
where  the  heights  of  the  dotted  lines  are  chosen  to  a  scale 
to  represent  proportionally  the  forces.  The  curve  which 


124  ELECTRICITY  AND   MAGNETISM        PART  i 

joins  the  tops  of  these  ordinates  shows  graphically  how 
the  force,  which  is  greatest  at  the  end,  falls  off  toward 
the  middle.  On  a  distant  magnet  pole  these  forces,  thus 
represented  by  this  curvilinear  triangle,  would  act  as  if 


N 

\ 


Fig.  SO. 

concentrated  at  a  point  in  the  magnet  opposite  the  "  centre 
of  gravity  "  of  this  triangle ;  or,  in  other  words,  the  "  pole," 
which  is  the  centre  of  the  resultant  forces,  is  not  at  the 
end  of  the  magnet.  In  thin  bars  of  magnetized  steel  it  is 
at  about  T^  of  the  magnet's  length  from  the  end. 

135.  Magnetic  Moment.  —  It  is  found  that  the  ten- 
dency of  a  magnet  to  turn  or  to  be  turned  by  another 
magnet  depends  not  only  on  the  strength  m  of  its  poles,  but 
the  length  I  between  them.   The  product  of  these  two  quan- 
tities m  x  Us  called  the  magnetic  moment  of  the  magnet, 
and  is  sometimes  denoted  by  the  symbol  M.     As  the  exact 
position  of  a  magnet's  poles  is  often  unknown,  it  is  easier 
to  determine  M  than  to  measure  either  m  or  /  separately. 

136.  Method  of  Deflexions.  —  There   are  a  number 
of  ways  in  which  the  deflexion  of  a  magnet  by  another 
magnet  may  be  made  use  of  to  measure  magnetic  forces.* 

*  The  student  desirous  of  mastering  these  methods  of  measuring  mag- 
netic forces  should  consult  Professor  Andrew  Gray's  Absolute  Measure- 
ments in  Electricity  and  Magnetism. 


CHAP.    II 


METHOD   OF  DEFLEXIONS 


125 


We  cannot  here  give  more  than  a  glance  at  first  principles. 
When  two  equal  and  opposite  forces  act  on  the  ends  of  a 
rigid  bar  they  simply  tend  to  turn  it  round.  Such  a  pair 
of  forces  form  what  is  called  a  "  couple,"  and  the  torque, 
or  tendency  to  turn  (formerly  called  the  "  moment "  of  the 
couple) ,  is  obtained  by  multiplying  one  of  the  two  forces 
by  the  perpendicular  distance  between  the  directions  of 
the  forces.  Such  a  couple  tends  to  produce  a  motion  of 
rotation,  but  not  a  motion  of  translation.  Now  a  mag- 
netic needle  placed  in  a 
magnetic  field  across  the 
lines  of  force  experiences 
a  torque,  tending  to  rotate 
it  round  into  the  magnetic 
meridian,  for  the  N-seek- 
ing  pole  is  urged  north- 
wards, and  the  S-seeking 
pole  is  urged  southwards, 
with  an  equal  and  opposite 
force.  The  force  acting 
on  each  pole  is  the  pro- 
duct of  the  strength  of  the 
pole  and  the  intensity  of 
the  "  field,"  that  is  to  say, 
of  the  horizontal  com- 
ponent of  the  force  of  the 


Fig.  81. 


earth's  magnetism  at  the 
place.  We  will  call  the 
strength  of  the  N-seeking  pole  m ;  and  we  will  use  the 
symbol  H  to  represent  the  force  which  the  earth's 
magnetism  would  exert  in  a  horizontal  direction  on 
a  unit  of  magnetism.  (The  value  of  H  is  different 
at  different  regions  of  the  globe.)  The  force  on  the 
pole  A  (see  Fig.  81)  will  be  then  m  x  H,  and  that  on 
pole  B  will  be  equal  and  opposite.  We  take  NS  as 
the  direction  of  the  magnetic  meridian  :  the  forces  will 
be  parallel  to  this  direction.  Now,  the  needle  AB  lies 


126  ELECTRICITY   AND   MAGNETISM        PART 


obliquely  in  the  field,  while  the  magnetic  force  acting  on 
A  is  in  the  direction  of  the  line  PA,  and  that  on  B  in 
the  direction  QB,  as  shown  by  the  arrows.  PQ  is  the 
perpendicular  distance  between  these  forces ;  hence  the 
"  moment "  of  the  couple,  or  torque,  will  be  got  by 
multiplying  the  length  PQ  by  the  force  exerted  on  one 
of  the  poles.  Using  the  symbol  Y  for  the  torque,  we 
may  write 

Y  =  PQ  x  m  •  H. 

But  PQ  is  equal  to  the  length  of  the  magnet  multiplied 
by  the  sine  *  of  the  angle  AOR,  which  is  the  angle  of 
deflexion,  and  which  we  will  call  8.  Hence,  using  I  for 
the  length  between  the  poles  of  the  magnet,  we  may 
write  the  expression  for  the  moment  of  the  couple. 

Y  =  mlH.  •  sin  5. 

In  words  this  is :  the  torque  acting  on  the  needle  is 
proportional  to  its  "magnetic  moment"  (m  x  /),  to  the 
horizontal  force  of  the  earth's  magnetism,  and  to  the  sine 
of  the  angle  of  deflexion. 

The  reader  will  not  have  failed  to  notice  that  if  the 
needle  were  turned  more  obliquely,  the  distance  PQ 
would  be  longer,  and  would  be  greatest  if  the  needle 
were  turned  round  east-and-west,  or  in  the  direction 
EW.  Also  the  torque  tending  to  rotate  the  magnet 
will  be  less  and  less  as  the  needle  is  turned  more  nearly 
into  the  direction  NS. 

137.  Law  of  Tangents .  —  Now,  let  us  suppose  that  the 
deflexion  8  were  produced  by  a  magnetic  force  applied  at 
right  angles  to  the  magnetic  meridian,  and  tending  to  draw 
the  pole  A  in  the  direction  R  A.  The  length  of  the  line  RT 
multiplied  by  the  new  force  will  be  the  leverage  of  the 
new  couple  tending  to  twist  the  magnet  into  the  direction 

*  If  any  reader  is  unacquainted  with  trigonometrical  terms  he  should 
consult  the  note  at  the  end  of  this  lesson,  on  "  Ways  of  Beckoning 
Angles." 


MAGNETOMETERS 


127 


EW.  Now,  if  the  needle  has  come  to  rest  in  equilibrium 
between  these  two  forces,  it  is  clear  that  the  two  opposing 
twists  are  just  equal  and  opposite  in  power,  or  that  the 
torque  due  to  one  couple  is  equal  to  that  of  the  other 
couple.  Hence  the  force  in  the  direction  WE  will  be  to 
the  force  in  the  direction  SN  in  the  same  ratio  as  PQ  is 
to  RT,  or  as  PO  is  to  RO. 

Or,  calling  this  force  f, 

f:  H  =  PO  :  RO. 

Or  /=Hg- 

But  PO  =  AR  and  g  =  tan  8,  hence 
/  =  H  tan  8 ; 

or,  in  other  words,  the  magnetic  force  which,  acting  at  right 
angles  to  the  meridian,  produces  on  a  magnetic  needle  the 
deflexion  8,  is  equal  to  the  horizontal  force  of  the  earth's 
magnetism  at  that  point,  multiplied  by  the  tangent  of  the 
angle  of  deflexion.  Hence,  also, 
two  different  magnetic  forces  act- 
ing at  right  angles  to  the  meridian 
would  severally  deflect  the  needle 
through  angles  whose  tangents  are 
proportional  to  the  forces. 

This  very  important  theorem 
is  applied  in  the  construction  of 
certain  galvanometers  (see  Art. 
212). 

138.  Magnetometers.  —  The 
name  Magnetometer  is  given  to 
any  magnet  specially  arranged 
as  an  instrument  for  the  purpose 
of  measuring  magnetic  forces. 
The  methods  of  observing  the 


«'••.'  \ 


Fig.  82. 


absolute  values  of   magnetic  forces  in  dyne-units    (units 
in  the  "  C.G.S."  system)  will  be  explained  in  Art.  361 


128  ELECTRICITY   AND   MAGNETISM        PART  i 

at  the  end  of  Lesson  XXVII.  Very  simple  magneto- 
meters, consisting  of  small  needles  pivoted,  or  suspended 
by  a  fibre,  are  commonly  used  for  measuring  the  relative 
values  of  magnetic  forces.  One  very  sensitive  form  (Fig. 
82),  to  be  used,  like  the  reflecting  galvanometer  (Art. 
215),  with  a  beam  of  light  as  a  pointer,  consists  of  a  small 

thin  silvered  glass  mir- 
ror, a  half -inch  or  less 
==-   in     diameter,     having 
two  or  three  very  light 
Fi    gg  magnets    cemented   at 

its  back,  suspended  by 

a  single  thread  of  cocoon  silk,  and  enclosed  in  a  suitable 
case.  Another  useful  form  (Fig.  83)  consists  of  a  short 
compass-needle  poised  on  a  pivot  having  a  light  index 
of  aluminium  long  enough  to  move  over  a  scale  divided 
into  tangent  values  (see  Art.  212). 

A  convenient  deflexion  magnetometer  for  comparing 
the  magnetic  moments    (Art.   135)  of  two  magnets  is 


First    Position. 
W 


afforded  by  such  a  tangent  compass  placed  in  the  middle 
of  a  graduated  platform  (Fig.  84).  There  are  two 
methods  of  using  this  apparatus. 

First  Position :  End-on  Method.  —  The  platform  being 
set  magnetically  east  and  west,  the  deflecting  magnet  is 
set  end-on.  Under  these  circumstances  the  force  is  found 
to  vary  directly  as  the  magnetic  moment  (Art.  135),  and 
inversely  as  the  cube  of  the  distance  between  the  centres  of 
the  magnets,  or  in  symbols  :  — 

/=2M  r*. 


CHAP.    II 


MAGNETOMETRIC   METHODS 


129 


But  we  have  seen  above  that  where  magnetic  force  is 
measured  by  a  deflexion  8  at  a  place  where  the  II  is 
earth's  horizontal  magnetic  force,  /  is  equal  to  H  tan  $  ; 
so  that 

2M/r3  =  H  tan  8, 
whence 

M  =    r*H  tan  S. 


Second  Position  :  Broadside-on.  —  The  platform  being 
turned  into  the  north-south  position,  the  deflecting 
magnet  is  set  broad  side-on.  In  this 
case  the  magnet  deflects  the  needle  in 
the  other  direction  and  with  half  the 
force  that  it  would  have  exerted  at  an 
equal  distance  in  the  end-on  position. 
But  the  force  still  varies  inversely  as 
the  cube  of  the  distance  :  the  formula 
being  now 

/=M/r*, 
whence 

M  =  r3II  tan  S. 


139.   Balance    Methods.  —  Tn 

either  position  of  the  magnetometer 
platform  two  magnets  can  be  placed 
on  the  two  sides  of  the  board  so  as  to 
balance  one  another's  effects  by  adjust- 
ing them  to  proper  distances.  This 
gives  a  comparison  of  their  magnetic 
moments  in  terms  of  their  respective 
distances,  or 


s 

Second 
Position 


Fig.  85. 


14O.  Hughes's  Magnetic  Balance. 
—  A  very  convenient  instrument  for  testing  the  mag- 
netic properties  of  different  specimens  of  iron  and  steel 
was  devised  by  Hughes  in  1884.  The  sample  to  be  tested 


130  ELECTRICITY  AND   MAGNETISM         PART  i 

is  placed  in  a  magnetizing  coil  A  (Fig.  86),  and  a  current 
is  sent  round  it.  It  deflects  a  lightly-suspended  indicating 
needle  B,  which  is  then  brought  to  zero  by  turning  a 
large  compensating  magnet  M  upon  its  centre.  A  small 
coil  C  is  added  to  balance  the  direct  deflecting  effect  due 


Fig.  86. 

to  coil  A.  The  author  of  this  book  has  shown  that  if  the 
distance  from  M  to  B  is  2-3  times  the  length  of  M,  the 
angle  through  which  M  is  turned  is  proportional  to 
the  magnetic  force  due  to  the  iron  core  at  A,  provided 
the  angle  is  less  than  60°. 

141.  Unit  Strength  of  Pole.  — The  Second  Law  of 
Magnetic  Force  (see  Art.  128)  stated  that  the  force  exerted 
between  two  poles  was  proportional  to  the  product  of 
their  strengths,  and  was  inversely  proportional  to  the 
square  of  the  distance  between  them.  It  is  possible  to 
choose  such  a  strength  of  pole  that  this  proportionality 
shall  become  numerically  an  equality.  In  order  that  this 
may  be  so,  we  must  adopt  the  following  as  our  unit  of 
strength  of  a  pole,  or  unit  magnetic  pole  :  A  Unit  Mag- 
netic Pole  is  one  of  such  a  strength  that,  when  placed  at  a 
distance  of  one  centimetre  from  a  similar  pole  of  equal 
strength  it  repels  it  with  a  force  of  one  dyne  (see  Art.  352). 
If  we  adopt  this  definition  we  may  express  the  second 
law  of  magnetic  force  in  the  following  equation  :  — 

f _m x  TO' 

J    -~' 


CHAP,  ii      THEORY   OF   MAGNETIC   CURVES          131 

where  f  is  the  force  (in  dynes),  m  and  in'  the  strengths  of 
the  two  poles,  and  d  the  distance  between  them  (in  centi- 
metres). From  this  definition  is  derived  the  arbitrary 
convention  about  magnetic  lines.  If  at  any  place  in  a 
magnetic  field  we  imagine  a  unit  magnetic  pole  to  be  set 
it  will  be  acted  upon,  tending  to  move  along  the  lines  of 
the  field.  Then  if  at  that  place  we  find  the  force  on  the 
pole  to  be  H  dynes,  we  may  conceive  that  there  are  H 
lines  drawn  per  square  centimetre.  For  example,  if  we 
describe  the  field  as  having  50  lines  side  by  side  per 
square  centimetre,  we  mean  that  a  unit  pole  placed  there 
will  be  acted  on  with  a  force  of  50  dynes.  This  subject 
is  resumed  in  Lesson  XXVI.,  Art.  338,  on  the  Theory  of 
Magnetic  Potential. 

142.  Theory  of  Magnetic  Curves.  — We  saw  (Art. 
119)  that  magnetic  figures  are  produced  by  iron  filings 
setting  themselves  in  certain  directions  in  the  field  of 
force  around  a  magnet.  We  can  now  apply  the  law  of 
inverse  squares  to  aid  us  in  determining  the  direction 
in  which  a  filing  will  set  itself  at  any  point  in  the 
field.  Let  NS  (Fig.  87)  be  a  long  thin  magnet,  and  P 
any  point  in  the  field  due  to  its  magnetism.  If  the  N- 
seeking  pole  of  a  small  magnet  be  put  at  P,  it  will  be 
attracted  by  S  and  repelled  by  N ;  the  directions  of  these 
two  forces  will  be  along  the  lines  PS  and  PN.  The 
amounts  of  the  forces  may  be  represented  by  certain 
lengths  marked  out  along  these  lines.  Suppose  the  dis- 
tance PN  is  twice  as  great  as  PS,  the  repelling  force  along 
PN  will  be  £  as  strong  as  the  attracting  force  along  PS. 
So  measure  a  distance  out,  PA  towards  S  four  times  as 
long  as  the  length  PB  measured  along  PN  away  from 
N.  Find  the  resultant  force  in  the  usual  way  of  com- 
pounding mechanical  forces,  by  completing  the  parallelo- 
gram PARE ;  the  diagonal  PR  represents  by  its  length 
and  direction  the  magnitude  and  the  direction  of  the 
resultant  magnetic  force  at  the  point  P.  In  fact  the  line 
PR  represents  the  line  along  which  a  small  magnet  or  an 


132  ELECTEICITY   AND   MAGNETISM       PART  i 

iron  filing  would  set  itself.  In  a  similar  way  we  might 
ascertain  the  direction  of  the  lines  of  force  at  any  point 
of  the  field.  The  little  arrows  in  Fig.  87  show  how  the 
lines  of  force  start  out  from  the  N  pole  and  curve  round 
to  meet  in  the  S  pole.  The  student  should  compare  this 


/  V 


\J  /  ;^ 

— >  ^'  •'••'''.  'r:::  :„.:  ^;-      '     '^j 

',N 


\ 


.  87. 


figure  with  the  lines  of  filings  of  Fig.  07.  Henceforth  we 
must  think  of  every  magnet  as  being  permeated  by  these 
magnetic  lines  which  extend  out  into  the  surrounding 
space.  The  whole  number  of  magnetic  lines  which  run 
through  a  magnet  is  termed  its  magnetic  flux  (Art.  337). 

143.  A  Magnetic  Paradox.  —  Tf  the  N-seeking  pole 
of  a  strong  magnet  be  held  at  some  distance  from  the 
N-seeking  pole  of  a  weak  magnet,  it  will  repel  it ;  but 
if  it  is  pushed  up  quite  close  it  will  be  found  now  to 
attract  it.  This  paradoxical  experiment  is  explained  by 
the  fact  that  the  magnetism  induced  in  the  weak  mag- 
net by  the  powerful  one  will  be  of  the  opposite  kind, 
and  will  be  attracted ;  and,  when  the  powerful  magnet 
is  near,  this  induced  magnetism  may  overpower  and 
mask  the  original  magnetism  of  the  weak  magnet.  The 


CHAP,  ii  BECKONING   OF   ANGLES  133 

student  must  be  cautioned  that  in  most  of  the  experi- 
ments on  magnet  poles  similar  perturbing  causes  are  at 
work.  The  magnetism  in  a  magnet  is  not  quite  fixed, 
but  is  liable  to  be  disturbed  in  its  distribution  by  the 
near  presence  of  other  magnet  poles,  for  no  steel  is  so 
hard  as  not  to  be  temporarily  affected  by  magnetic 
induction. 

NOTE   ON  WAYS   OF  RECKONING  ANGLES   AND   SOLID 
ANGLES 

144.  Reckoning  in  Degrees.  —  When  two  straight  lines  cross 
one  another  they  form  an  angle  between  them ;  and  this  angle 
may  be  defined  as  the  amount  of  rotation  which  one  of  the  lines 
has  performed  round  a  fixed  point  in 

the  other  line.  Thus  we  may  suppose 
the  line  CP  in  Fig.  88  to  have  originally 
lain  along  CO,  and  then  turned  round 
to  its  present  position.  The  amount  by 
which  it  has  been  rotated  is  clearly  a  cer- 
tain fraction  of  the  whole  way  round ; 
and  the  amount  of  rotation  round  C  we 
call  "  the  angle  which  PC  makes  with 
OC,"  or  more  simply  "  the  angle  PCO." 
But  there  are  a  number  of  different 
ways  of  reckoning  this  angle.  The 
common  way  is  to  reckon  the  angle  by 

"  degrees  "  of  arc.  Thus,  suppose  a  circle  to  be  drawn  round  C, 
if  the  circumference  of  the  circle  were  divided  into  360  parts 
each  part  would  be  called  "  one  degree  "  (1°),  and  the  angle 
would  be  reckoned  by  naming  the  number  of  such  degrees  along 

the  curved  arc  OP.    In  the  figure  the  arc  is  about  571°,  or  ~* 

360 
of  the  whole  way  round,  no  matter  what  size  the  circle  is  drawn. 

145.  Reckoning  in  Radians.  —  A  more  sensible  but  less  usual 
way  to  express  an  angle  is  to  reckon  it  by  the  ratio  between  the 
length  of  the  curved  arc  that  ''subtends"  the  angle  and  the 
length  of  the  radius  of  the  circle.    Suppose  we  have  drawn  round 
the  centre  C  a  circle  whose  radius  is  one  centimetre,  the  diam- 
eter will  be  two  centimetres.    The  length  of  the  circumference 
all  round  is  known  to  be  about  3J  times  the  length  of  the  diam- 
eter, or  more  exactly  3' 14159.  .  .  .    This  number  is  so  awkward 


134 


ELECTRICITY   AND   MAGNETISM       PART  i 


that,  for  convenience,  we  always  use  for  it  the  Greek  letter  n. 
Hence  the  length  of  the  circumference  of  our  circle,  whose  radius 
is  one  centimetre,  will  be  6'28318  .  .  .  centimetres,  or  2ir  centi- 
metres. We  can  then  reckon  any  angle  by  naming  the  length  of 
arc  that  subtends  it  on  a  circle  one  centimetre  in  radius.  If  we 
choose  the  angle  PCO,  such  that  the  curved  arc  OP  shall  be  just 
one  centimetre  long,  this  will  be  the  angle  one,  or  unit  of  angular 
measure,  or,  as  it  is  sometimes  called,  the  angle  PCO  will  be  one 

300° 
"  radian."  In  degree-measure  one  radian  = =  57°  17'  nearly. 

All  the  way  round  the  circle  will  be  2n  radians.  A  right  angle 
will  be  I  radians. 

146.  Reckoning    by  Sines    or    Cosines.  —  In   trigonometry 

other  ways  of  reckoning  angles  are  used,  in  which,  however,  the 
angles  themselves  are  not  reckoned,  but 
certain  "functions  "  of  them  called  "sines," 
"cosines,"  "tangents,"  etc.  For  readers 
not  accustomed  to  these  we  will  briefly 
explain  the  geometrical  nature  of  these 
"  functions."  Suppose  we  draw  (Fig.  89) 
our  circle  as  before  round  centre  C,  and 
then  drop  down  a  plumb-line  PM,  on  to  the 
line  CO ;  we  will,  instead  of  reckoning  the 
angle  by  the  curved  arc,  reckon  it  by  the 
length  of  the  line  PM.  It  is  clear  that 

if  the  angle  is  small,  PM  will  be  short ;  but  as  the  angle  opens 

out  towards  a  right  angle,  PM  will  get  longer  and  longer  (Fig. 

90) .    The  ratio  between  the  length  of  this  line  and  the  radius 

of  the  circle  is  called  the  "  sine  "   of  the 

angle,  and  if  the  radius  is  1  the  length  of 

PM  will  be  the  value  of  the  sine.    It  can 

never  be  greater  than  1,   though  it  may 

have  all  values  between  1  and— 1.     The 

length  of  the  line  CM  will  also  depend  upon 

the  amount  of  the  angle.     If  the  angle  is 

small  CM  will  be  nearly  as  long  as  CO; 

if  the  angle  open  out  to  nearly  a  right  angle 

CM  will  be  very  short.    The  length  of  CM  (when  the  radius  is  1) 

is  called  the  "  cosine  "  of  the  angle.  If  the  angle  be  called  0,  then 

we  may  for  shortness  write  these  functions : 


Fig.  89. 


Fig.  90. 


"-•- $ 


CHAP.    II 


SOLID  ANGLES 


136 


M 


Fig.  91. 


147.  Reckoning  by  Tangents.  — Suppose  we  draw  our  circle 
as  before  (Fig.  91) ,  but  at  the  point  O  draw  a  straight  line  touch- 
ing the  circle,  the  tangent  line  at  O ;  let  us 

also  prolong  CP  until  it  meets  the  tangent 
line  at  T.  We  may  measure  the  angle 
between  OC  and  OP  in  terms  of  the  length 
of  the  tangent  OT  as  compared  with  the 
length  of  the  radius.  Since  our  radius  is 
1,  this  ratio  is  numerically  the  length  of 
OT,  and  we  may  therefore  call  the  length 
of  OT  the  "  tangent "  of  the  angle  OCP. 
It  is  clear  that  smaller  angles  will  have  / 
smaller  tangents,  but  that  larger  angles  j 
may  have  very  large  tangents;  in  fact,  \ 
the  length  of  the  tangent  when  PC  was 
moved  round  to  a  right  angle  would  be 
infinitely  great.  It  can  be  shown  that  the 
ratio  between  the  lengths  of  the  sine  and 
of  the  cosine  of  the  angle  is  the  same  as 

the  ratio  between  the  length  of  the  tangent  and  that  of  the 
radius ;  or  the  tangent  of  an  angle  is  equal  to  its  sine  divided 
by  its  cosine.  The  formula  for  the  tangent  may  be  written  : 

>  =  PM 

i    MC* 

148.  Solid  Angles.— When  three  or  more  surfaces  inter- 
sect at  a  point  they  form  a  solid  angle  :  there  is  a  solid  angle, 

for  example,  at  the  top  of  a 
pyramid,  or  of  a  cone,  and  one 
at  every  corner  of  a  diamond 
that  has  been  cut.  If  a  surface 
of  any  given  shape  be  near  a 
point,  it  is  said  to  subtend  a 
certain  solid  angle  at  that 
point,  the  solid  angle  being 
mapped  out  by  drawing  lines 
from  all  points  of  the  edge  of 
this  surface  to  the  point  P  (Fig. 
92).  An  irregular  cone  will 
thus  be  generated  whose  solid 
angle  is  the  solid  angle  sub- 
tended at  P  by  the  surface  EF.  To  reckon  this  solid  angle  we 
adopt  an  expedient  similar  to  that  adopted  when  we  wished 
to  reckon  a  plane  angle  in  radians.  About  the  point  P,  with 
radius  of  1  centimetre,  describe  a  sphere,  which  will  intercept 


Fig.  92. 


136 


ELECTRICITY  AND   MAGNETISM        PART  i 


the  cone  over  an  area  MN :  the  area  thus  intercepted  measures 
the  solid  angle.  If  the  sphere  have  the  radius  1,  its  total  surface 
is  47T.  The  solid  angle  subtended  at  the  centre  by  a  hemisphere 
would  be  27T.  It  will  be  seen  that  the  ratio  between  the  area  of 
the  surface  EF  and  the  area  of  the  surface  MN  is  the  ratio 
between  the  squares  of  the  lines  EP  and  MP.  The  solid  angle 
subtended  by  a  surface  at  a  point  (other  things  being  equal)  is 
inversely  proportional  to  the  square  of  its  distance  from  the 
point.  This  is  the  basis  of  the  law  of  inverse  squares. 

A  table  of  radians,  sines,  tangents,  etc.,  is  given  at  the  end 
of  this  book  as  Appendix  A. 


LESSON  XII.  —  Terrestrial  Magnetism 

149.   The    Mariner's   Compass.  —  It  was   mentioned 
in  Art.  87  that  the  compass  sold  by  opticians  consists  of 


Fig.  93. 


a  magnetized  steel  needle  balanced  on  a  fine  point  above 
a  card   marked  out   N,    S,   E,   W,   etc.     The   Mariner's 
Compass  is,  however,  somewhat  differently  arranged. 
In  Fig.  93  one  of  the  forms  of  a  Mariner's  Compass, 


CHAP,  ii         TERRESTRIAL  MAGNETISM  137 

used  for  nautical  observations,  is  shown.  Here  the  card, 
divided  out  into  the  32  "  points  of  the  compass,"  is  itself 
attached  to  the  needle,  and  swings  round  with  it  so  that 
the  point  marked  N  on  the  card  always  points  to  the 
north.  In  the  best  modern  ships'  compasses,  such  as 
those  of  Lord  Kelvin,  several  magnetized  needles  are 
placed  side  by  side,  as  it  is  found  that  the  indications  of 
such  a  compound  needle  are  more  reliable.  The  iron 
fittings  of  wooden  vessels,  and,  in  the  case  of  iron  vessels, 
the  ships  themselves,  affect  the  compass,  which  has  there- 
fore to  be  corrected  by  placing  compensating  masses  of 
iron  near  it,  or  by  fixing  it  high  upon  a  mast.  The 
error  of  the  compass  due  to  magnetism  of  the  ship  is 
known  as  the  deviation. 

150.  The  Earth  a  Magnet.  —  Gilbert  made  the  great 
discovery  that  the  compass-needle  points  north  and  south 
because  the  earth   is   itself  also  a  great  magnet.     The 
magnetic  poles  of  the  earth  are,  however,  not  exactly  at 
the  geographical  north  and  south  poles.     The  magnetic 
north  pole  of   the  earth  is  more  than  1000  miles  away 
from  the  actual  pole,  being  in  lat.  70°  5'  N.,  and  long. 
96°  46'  W.     In  1831,  it  was  found  by  Sir  J.  C.  Ross  to 
be  situated    in   Boothia  Felix,   just  within   the   Arctic 
Circle.     The  south  magnetic  pole  of  the  earth  has  never 
been   reached ;   and  by  reason  of  irregularities  in   the 
distribution  of   the   magnetism  there  appear  to  be  two 
south  magnetic  polar  regions. 

151.  Declination.  —  In   consequence  of   this   natural 
distribution  the  compass-needle  does  not  at  all  points  of 
the  earth's  surface  point  truly  north  and  south.    Thus,  in 
1894,  the  compass-needle  at  London  pointed  at  an  angle 
of  about  17°  west  of  the  true  north ;  in  1900  it  will  be 
16°  16'.     This  angle  between  the  magnetic  meridian  *  and 

*  The  Magnetic  Meridian  of  any  place  is  an  imaginary  plane  drawn 
through  the  zenith,  and  passing  through  the  magnetic  north  point  and 
magnetic  south  point  of  the  horizon,  as  observed  at  that  place  by  the 
pointing  of  a  horizontally-suspended  compass-needle. 


138 


ELECTRICITY  AND   MAGNETISM        PART 


the  geographical  meridian  of  a  place  is  called  the  magnetic 
Declination  of  that  place.  The  existence  of  this  declina- 
tion was  discovered  by  Columbus  in  1492,  though  it 
appears  to  have  been  previously  known  to  the  Chinese, 
and  is  said  to  have  been  noticed  in  Europe  in  the  early 
part  of  the  thirteenth  century  by  Peter  Peregrinus.  The 
fact  that  the  declination  differs  at  different  points  of  the 
earth's  surface,  is  the  undisputed  discovery  of  Columbus. 
In  order  that  ships  may  steer  by  the  compass,  magnetic 
charts  (Art.  154)  must  be  prepared,  and  the  declination  at 
different  places  accurately  measured.  The  upright  pieces 
P,  P',  on  the  "  azimuth  compass  "  drawn  in  Fig.  93,  are 
for  the  purpose  of  sighting  a  star  whose  position  may 
be  known  from  astronomical  tables,  and  thus  affording 

a  comparison  be- 
tween the  magnetic 
meridian  of  the 
place  and  the  geo- 
graphical meridian, 
and  of  measuring 
the  angle  between 
them. 

152.  Inclina- 
tion or  Dip.  —  Nor- 
man, an  instru- 
ment -  maker,  dis- 
covered in  1576 
that  a  balanced 
needle,  when  mag- 
netized, tends  to 
dip  downwards  to- 
ward the  north. 
He  therefore  con- 
structed a  Dip- 
ping-Needle,  capa- 
ble of  turning  in  a  vertical  plane  about  a  horizontal  axis, 
with  which  he  found  the  "  dip "  to  be  (at  London)  an 


Fig.  94. 


CHAP.    II 


MAGNETIC   DIP 


139 


angle  of  71°  50'.  A  simple  form  of  dipping-needle  is 
shown  in  Fig.  94.  The  dip-circles  used  in  the  magnetic 
observatory  at  Kew  are  much  more  exact  and  delicate 
instruments.  It  was,  however,  found  that  the  dip,  like 
the  declination,  differs  at  different  parts  of  the  earth's 
surface,  and  that  it  also  undergoes  changes  from  year  to 
year.  The  "  dip  "  in  London  for  the  year  1894  is  67°  18' ; 
in  1900  it  will  be  67°  9'.  At  the  north  magnetic  pole 
the  needle  dips  straight  down.  The  following  table 
gives  particulars  of  the  Declination,  Inclination,  and 
total  magnetic  force  at  a  number  of  important  places, 
the  values  being  approximately  true  for  the  year  1900. 


TABLE  OP  MAGNETIC  DECLINATION  AND  INCLINATION 
(for  Year  1900) 


Locality. 

Declination. 

Dip. 

Total  Force 
(C.G.S.). 

London    .... 
St.  Petersburg  . 
Berlin    .  .  . 

16°  16'  W. 
0°  30'  E. 
9°  30'  W 

67°  9'    N. 
70°  46'  N. 
66°  43'  N 

0-47 

0-48 
0-48 

Paris  
Rome    
New  York  .  .  . 
Washington  .  . 
San  Francisco  . 
Mexico  

14°  30'  W. 
10°  0'    W. 
9°  12'  W. 
4°  35'  W. 
16°  42'  E. 
8°  0'    E. 

64°  55'  N. 
58°  0'    N. 
70°  6'    N. 
70°  18'  N. 
62°  20'  N. 
45°  1'    N 

0-47 
0-45 
0-61 
0-60 
0-54 
0-48 

St.  Helena  .  .  . 
Cape  Town    .  . 
Sydney    .... 
Hobarton    .   .  . 
Bombay  .... 
Tokio    

25°  0'    W. 
29°  24'  W. 
9°  36'  E. 
25°  0'    E. 
0°  36'  E. 
4°  6'    W. 

32°  12'  S. 
58°  2'    S. 
62°  45'  S. 
71°  12'  S. 
20°  38'  N. 
49°  52'  N. 

0-31 
0-36 
0-57 
0-64 
0-37 
0-45 

153.  Intensity.  —  Three  things  must  be  known  in 
order  to  specify  exactly  the  magnetism  at  any  place ; 
these  three  elements  are : 


140  ELECTRICITY   AND   MAGNETISM        PART  i 

The  Declination ; 

The  Inclination,  and 

The  Intensity  of  the  Magnetic  Force. 

The  magnetic  force  is  measured  by  one  of  the  methods 
mentioned  in  the  preceding  lesson.  Its  direction  is  in 
the  line  of  the  dipping-needle,  which,  like  every  magnet, 
tends  to  set  itself  along  the  lines  of  force.  It  is,  however, 
more  convenient  to  measure  the  force  not  in  its  total 
intensity  in  the  line  of  the  dip,  but  to  measure  the 
horizontal  component  of  the  force,  —  that  is  to  say,  the 
force  in  the  direction  of  the  horizontal  compass-needle, 
from  which  the  total  force  can  be  calculated  if  the  dip  is 
known.*  Or  if  the  horizontal  and  vertical  components  of 
the  force  are  known,  the  total  force  and  the  angle  of  the 
dip  can  both  be  calculated.!  The  horizontal  component 
of  the  force,  or  "  horizontal  intensity,"  can  be  ascertained 
either  by  the  method  of  Vibrations  or  by  the  method  of 
Deflexions.  The  mean  horizontal  force  of  the  earth's 
magnetism  at  London  in  1890  was  -1823  dyne-units,  the 
mean  vertical  force  -4377,  the  total  force  (in  the  line  of  dip) 
was  4741  dyne-units.  The  distribution  of  the  magnetic 
force  at  different  points  of  the  earth's  surface  is  irregular, 
and  varies  in  different  latitudes  according  to  an  approxi- 
mate law,  which,  as  given  by  Biot,  is  that  the  force  is  pro- 
portional to  VI  +  3  sin2/,  where  I  is  the  magnetic  latitude. 

154.  Magnetic  Maps.  —  For  purposes  of  convenience 
it  is  usual  to  construct  magnetic  maps,  on  which  such 
data  as  these  given  in  the  Table  on  p.  139  can  be  marked 
down.  Such  maps  may  be  constructed  in  several  ways. 
Thus,  it  would  be  possible  to  take  a  map  of  England,  or 
of  the  world,  and  mark  it  over  with  lines  such  as  to 
represent  by  their  direction  the  actual  direction  in  which 
the  compass  points  ;  in  fact  to  draw  the  lines  of  force  or 

*  For  if  H  =  Horizontal  Component  of  Force,  and  I  =  Total  Force,  and 
6  =  angle  of  dip,  I  =  H  f-  cos  0. 

t  For  H3  +  V2  =  I2,  where  V  =  Vertical  Component  of  Force. 


CHAP,  ii  MAGNETIC   MAPS  141 

magnetic  meridians.  A  more  useful  way  of  marking  the 
map  is  to  find  out  those  places  at  which  the  declination 
is  the  same,  and  to  join  these  places  by  a  line.  The 
Magnetic  Map  of  Great  Britain,  which  forms  the  Frontis- 
piece to  these  lessons,  is  constructed  on  this  plan  from  the 
magnetic  survey  lately  made  by  RUcker  and  Thorpe.  At 
Plymouth  the  compass-needle  in  1900  will  point  18°  to 
the  west  of  the  geographical  north.  The  declination  at 
Lynton,  at  Shrewsbury,  and  at  Berwick  will  in  that  year 
be  the  same  as  at  Plymouth.  Hence  a  line  joining  these 
towns  may  be  called  a  line  of  equal  declination,  or  an 
Isogonic  line.  It  will  be  seen  from  this  map  that  the 
declination  is  greater  in  the  north-west  of  England  than 
in  the  south-east.  We  might  similarly  construct  a  mag- 
netic map,  marking  it  with  lines  joining  places  where  the 
dip  was  equal ;  such  lines  would  be  called  Isoclinic  lines. 
In  England  they  run  across  the  map  from  west-south-west 
to  east-north-east.  For  example,  in  1900  the  needle  will 
dip  about  67°  at  London,  Southampton,  and  Plymouth. 
Through  these  places  then  the  isoclinic  of  67°  may  be 
drawn  for  that  epoch.  On  the  globe  the  isogonic  lines 
run  for  the  most  part  from  the  north  magnetic  pole  to  the 
south  magnetic  polar  region,  but,  owing  to  the  irregulari- 
ties of  distribution  of  the  earth's  magnetism,  their  forms 
are  not  simple.  The  isoclinic  lines  of  the  globe  run  round 
the  earth  like  the  parallels  of  latitude,  but  are  irregular 
in  form.  Thus  the  line  joining  places  where  the  north- 
seeking  pole  of  the  needle  dips  down  70°  runs  across 
England  and  Wales,  passes  the  south  of  Ireland,  then 
crosses  the  Atlantic  in  a  south-westerly  direction,  traverses 
the  United  States,  swerving  northwards,  and  just  crosses 
the  southern  tip  of  Alaska.  It  drops  somewhat  southward 
again  as  it  crosses  China,  but  again  curves  northwards  as 
it  enters  Russian  territory.  Finally  it  crosses  the  south- 
ern part  of  the  Baltic,  and  reaches  England  across  the 
German  Ocean.  The  magnetic  chart  of  the  United 
States,  which  is  also  given  at  the  front  of  this  book,  is  for 


142  ELECTRICITY   AND   MAGNETISM        PART  i 

the  year  1900.  It  has  been  prepared  from  data  furnished 
by  Professor  Mendenhall  of  the  U.S.  Geodetic  Survey. 
It  will  be  noticed  that  in  the  year  1900  the  magnetic 
declination  will  be  zero  at  Lansing  (Mich.),  Columbus 
(Ohio),  and  Charleston  (S.  Carolina). 

The  line  passing  through  places  of  no  declination  is 
called  the  agonic  line.  It  passes  across  both  hemispheres, 
crossing  Russia,  Persia,  and  Australia.  There  is  another 
agonic  line  in  eastern  Asia  enclosing  a  region  around 
Japan,  within  which  there  is  a  westerly  declination. 

155.  Variations  of  Earth's  Magnetism.  —  We  have 
already  mentioned  that  both  the  declination  and  the 
inclination  are  subject  to  changes ;  some  of  these  changes 
take  place  very  slowly,  others  occur  every  year,  and  others 
again  every  day. 

Those  changes  which  require  many  years  to  run  their 
course  are  called  secular  changes. 

The  variations  of  the  declination  previous  to  1580  are 
not  recorded ;  the  compass  at  London  then  pointed  11° 
east  of  true  north.  This  easterly  declination  gradually 
decreased,  until  in  1657  the  compass  pointed  true  north. 
It  then  moved  westward,  attaining  a  maximum  of  24°  27' 
about  the  year  1816,  from  which  time  it  has  slowly  dimin- 
ished to  its  present  value  (16°  57'  in  1894)  ;  it  diminishes 
(in  England)  at  about  the  rate  of  7'  per  year.  At  about 
the  year  1976  it  will  again  point  truly  north,  making  a 
complete  cycle  of  changes  in  about  320  years. 

The  Inclination  in  1576  was  71°  50',  and  it  slowly 
increased  till  1720,  when  the  angle  of  dip  reached  the 
maximum  value  of  74°  42'.  It  has  since  steadily  dimin- 
ished to  its  present  (1894)  value  of  67°  39'.  The  period 
in  which  the  cycle  is  completed  is  not  known,  but  the  rate 
of  variation  of  the  dip  is  less  at  the  present  time  than  it 
was  fifty  years  ago.  In  all  parts  of  the  earth  both 
declination  and  inclination  are  slowly  changing.  The 
following  table  gives  the  data  of  the  secular  changes  at 
London. 


CHAP.    II 


MAGNETIC  VARIATION 


143 


TABLE  OF  SECULAR  MAGNETIC  VARIATIONS 


Year. 

Declination. 

Inclination. 

1576. 

71°  50' 

1580 

11°  17'  E. 

1600 

72°  0' 

1622 

6°  12' 

1634 

4°0' 

1657 

0°  0'  min. 

1676 

3°  0'  W. 

73°  30' 

1705 

9°0' 

1720 

13°  0' 

74°  42'  max. 

1760 

19°  30' 

1780 

72°  8' 

1800 

24°  6' 

70°  35' 

1816 

24°  30'  max. 

1830 

24°  2' 

69°  3' 

1855 

23°  0' 

1868 

20°  33' 

68°  2' 

1878 

19°  14' 

67°  43' 

1880 

18°  40' 

67°  40' 

1890 

17°  26' 

67°  23' 

1900 

16°  16' 

67°  9' 

The  Total  Magnetic  force,  or  "  Intensity,"  also  slowly 
changes  in  value.  As  measured  near  London,  it  was 
equal  to  -4791  dyne-units  in  1848,  4740  in  1866,  in 
1880  -4736  dyne-units,  in  1890  4741.*  Owing  to  the 
steady  decrease  of  the  angle  at  which  the  needle  dips, 
the  horizontal  component  of  this  force  (i.e.  the  "  Hori- 
zontal Intensity")  is  slightly  increasing.  It  was  '1716 
dyne-units  in  1814,  -1797  dyne-units  at  the  beginning  of 
1880,  and  -1823  dyne-units  in  1890. 

156.  Daily  Variations. — Both  compass  and  dipping- 
needle,  if  minutely  observed,  exhibit  slight  daily  mo- 

*  That  is  to  say,  a  north  magnet  pole  of  unit  strength  is  urged  in  the 
line  of  dip,  with  a  mechanical  force  of  a  little  less  than  half  a  dyne. 


144  ELECTRICITY  AND  MAGNETISM        PART  i 

tions.  About  7  A.M.  the  compass-needle  begins  to  travel 
westward  with  a  motion  which  lasts  till  about  1  P.M.  ; 
during  the  afternoon  and  evening  the  needle  slowly 
travels  back  eastward,  until  about  10  P.M.  ;  after  this 
it  rests  quiet ;  but  in  summer-time  the  needle  begins 
to  move  again  slightly  to  the  west  at  about  midnight, 
and  returns  again  eastward  before  7  A.M.  These  delicate 
variations  —  never  more  than  10'  of  arc  —  appear  to 
be  connected  with  the  position  of  the  sun ;  and  the  moon 
also  exercises  a  minute  influence  upon  the  position  of 
the  needle. 

157.  Annual  Variations.  —  There  is  also  an  annual 
variation  corresponding  with  the  movement  of  the  earth 
around  the  sun.     In  the  British  Islands  the  total  force 
is  greatest  in  June  and  least  in   February,  but  in  the 
Southern  Hemisphere,  in    Tasmania,  the  reverse  is  the 
case.     The  dip  also  differs  with  the  season  of  the  year, 
the  angle  of  dip  being  (in  England)  less  during  the  four 
summer  months  than  in  the  rest  of  the  year. 

158.  Eleven -Year     Period.  —  General    Sabine    dis- 
covered that  there  is   a  larger  amount  of  variation  of 
the  declination  occurring  about  once  every  eleven  years. 
Sclrwabe  noticed  that  the  recurrence   of  these  periods 
coincided  with  the  eleven-year  periods   at  which  there 
is  a  maximum  of  spots  on  the  sun.     Professor  Balfour 
Stewart  and  others  have  endeavoured  to  trace  a  similar 
periodicity  in  the   recurrence  of  aurorae  *  and  of  other 
phenomena. 

159.  Magnetic  Storms.  —  It  is  sometimes  observed 
that  a  sudden  (though  very  minute)  irregular  disturbance 
will  affect  the  whole  of  the  compass-needles  over  a  con- 
siderable region  of  the   globe.      Such   occurrences   are 
known  as  magnetic  storms ;  they  frequently  occur  at  the 
time  when  an  aurora  is  visible. 

160.  Self-recording  Magnetic  Apparatus.  —  At  Kew 
and  other  magnetic  observatories  the  daily  and  hourly 

*  See  Lesson  XXIV.,  on  Atmospheric  Electricity. 


CHAP,  ii         TERRESTRIAL   MAGNETISM  145 

variations  of  the  magnet  are  recorded  on  a  continuous 
register.  The  means  employed  consists  in  throwing  a 
beam  of  light  from  a  lamp  on  to  a  light  mirror  attached 
to  the  magnet  whose  motion  is  to  be  observed.  A  spot 
of  light  is  thus  reflected  upon  a  ribbon  of  photographic 
paper  prepared  so  as  to  be  sensitive  to  light.  The  paper 
is  moved  continuously  forward  by  a  clockwork  train ; 
and  if  the  magnet  be  at  rest  the  dark  trace  on  the  paper 
will  be  simply  a  straight  line.  If,  however,  the  magnet 
moves  aside,  the  spot  of  light  reflected  from  the  mirror 
will  be  displaced,  and  the  photographed  line  will  be 
curved  or  crooked.  Comparison  of  such  records,  or 
magnetographs,  from  stations  widely  apart  on  the  earth's 
surface,  promises  to  afford  much  light  upon  the  cause  of 
the  changes  of  the  earth's  magnetism,  to  which  hitherto 
no  reliable  origin  has  been  with  certainty  assigned. 
Schuster  has  shown  that  these  changes  generally  come 
from  without,  and  not  from  within. 

161.  Theory  of  Earth's  Magnetism.  —  The  phenome- 
non of  earth-currents  (Art.  233)  appears  to  be  con- 
nected with  that  of  the  changes  in  the  earth's  magnet- 
ism, and  can  be  observed  whenever  there  is  a  display  of 
aurora,  and  during  a  magnetic  storm ;  but  it  is  not  yet 
determined  whether  these  currents  are  due  to  the  varia- 
tions in  the  magnetism  of  the  earth,  or  whether  these 
variations  are  due  to  the  currents.  It  is  known  that  the 
evaporation  (see  Art.  71)  always  going  on  in  the  tropics 
causes  the  ascending  currents  of  heated  air  to  be  electri- 
fied positively  relatively  to  the  earth.  These  air-currents 
travel  northward  and  southward  toward  the  colder  polar 
regions,  where  they  descend.  These  streams  of  electri- 
fied air  will  act  (see  Art.  397)  like  true  electric  currents, 
and  as  the  earth  rotates  within  them  it  will  be  acted 
upon  magnetically.  The  author  has  for  twelve  years 
upheld  the  view  that  this  thermodynamic  production 
of  polar  currents  in  conjunction  with  the  earth's  diurnal 
rotation  affords  the  only  rational  means  yet  suggested 


146  ELECTRICITY   AND   MAGNETISM        PART  i 

for  accounting  for  the  growth  of  the  earth's  magnetism 
to  its  present  state.  The  action  of  the  sun  and  moon 
in  raising  tides  in  the  atmosphere  might  account  for  the 
variations  mentioned  in  Art.  155.  It  is  important  to 
note  that  in  all  magnetic  storms  the  intensity  of  the 
perturbations  is  greatest  in  the  regions  nearest  the  poles ; 
also,  that  the  magnetic  poles  coincide  very  nearly  with 
the  regions  of  greatest  cold ;  that  the  region  where 
aurorse  (Art.  336)  are  seen  in  greatest  abundance  is  a 
region  lying  nearly  symmetrically  round  the  magnetic 
pole.  It  may  be  added  that  the  general  direction  of  the 
feeble  daily  earth-currents  (Art.  233)  is  from  the  poles 
toward  the  equator. 


CHAPTER   III 


CURRENT    ELECTRICITY 

LESSON  XIII.  —  Simple  Voltaic  Cells 

162.  Flow  of  Currents.  —  It  has  been  already  men- 
tioned, in  Lesson  IV.,  how  electricity  flows  away  from 
a  charged  body  through  any  conducting  substance,  such 
as  a  wire  or  a  wetted  string.  If,  by  any  arrangement, 
electricity  could  be  supplied  to  the  body  just  as  fast  as 
it  flowed  away,  a  continuous  current  would  be  produced. 
Such  a  current  always  flows  through  a  conducting  wire, 
if  the  ends  are  kept  at  different  electric  potentials.  In 
like  manner,  a  current  of  heat  flows  through  a  rod  of 
metal  if  the  ends  are  kept  at  different  temperatures,  the 
flow  being  always  from  the  high  temperature  to  the 
lower.  No  exact  evidence  exists  as  to  the  direction  in 
which  the  current  in  a  wire  really  "flows."  It  is  con- 
venient to  regard  the  electricity  as  flowing  from  positive 
to  negative ;  or,  in  other  words,  the  natural  direction 
of  an  electric  current  is  from  the  high  potential  to  the 
low.  It  is  obvious  that  such  a  flow  tends  to  bring  both 
to  one  level  of  potential.  In  order  that  a  continuous 
flow  may  be  kept  up  there  must  be  a  circuit  provided. 
The  "  current "  has  sometimes  been  regarded  as  a  double 
transfer  of  positive  electricity  in  one  direction,  and  of 
negative  electricity  in  the  opposite  direction.  The  only 
evidence  to  support  this  very  unnecessary  supposition 
147 


148  ELECTRICITY   AND   MAGNETISM.       PART  i 

is  the  fact  that,  in  the  decomposition  of  liquids  by  the 
current,  some  of  the  elements  are  liberated  at  the  place 
where  the  current  enters,  others  at  the  place  where  it 
leaves  the  liquid. 

The  quantity  of  electricity  conveyed  by  a  current  is 
proportional  to  the  current  and  to  the  time  that  it  con- 
tinues to  flow.  The  practical  unit  of  current  is  called  the 
ampere  (see  Arts.  207  and  254).  The  quantity  of  electri- 
city conveyed  by  a  current  of  one  ampere  in  one  second  is 
called  one  ampere-second  or  one  coulomb.  One  ampere- 
hour  equals  3600  coulombs.  If  C  is  the  number  of 
amperes  of  current,  t  the  number  of  seconds  that  it  lasts, 
and  Q  the  number  of  coulombs  of  electricity  thereby  con- 
veyed, the  relation  between  them  is  expressed  by  the 
formula :  — 

Q  =  C  x  t. 

Example.  —  If  a  current  of  80  amperes  flows  for  15  minutes 
the  total  quantity  of  electricity  conveyed  will  be 
80  X  15  X  60  =  72,000  coulombs.  This  is  equal  to  20 
ampere-hours. 

Currents  are  called  continuous  if  they  flow,  without 
stopping,  in  one  direction.  They  are  called  alternate 
currents  if  they  continually  reverse  in  direction  in  a 
regular  periodic  manner,  flowing  first  in  one  direction 
round  the  circuit  and  then  in  the  other. 

Continuous  currents  of  electricity,  such  as  we  have 
described,  are  produced  by  voltaic  cells,  and  batteries  of 
such  cells,  or  else  by  dynamos  driven  by  power,  though 
there  are  other  sources  of  currents  hereafter  to  be  men- 
tioned. Alternate  currents  are  produced  by  special 
alternate  current  dynamos  or  alternators,  and  are  sepa- 
rately treated  of  in  Art.  470. 

163.  Discoveries  of  Galvani  and  of  Volta.  —  The  dis- 
covery of  electric  currents  originated  with  Galvani,  a 
physician  of  Bologna,  who,  about  the  year  1786,  made  a 
series  of  curious  and  important  observations  upon  the 


CHAP.    Ill 


THE   VOLTAIC    PILE 


149 


convulsive  motions  produced  by  the  "return-shock"  (Art. 
29)  and  other  electric  discharges  upon  a  frog's  leg.  He 
was  led  by  this  to  the  discovery  that  it  was  not  necessary 
to  use  an  electric  machine  to  produce  these  effects,  but 
that  a  similar  convulsive  kick  was  produced  in  the  frog's 
leg  when  two  dissimilar  metals,  iron  and  copper,  for 
example,  were  placed  in  contact  with  a  nerve  and  a 
muscle  respectively,  and  then  brought  into  contact  with 
each  other.  Galvani  imagined  this  action  to  be  due  to 
electricity  generated  by  the  frog's  leg  itself.  It  was, 
however,  proved  by  Volta,  Professor  in  the  University 
of  Pavia,  that  the  electricity  arose  not  from  the  muscle 
or  nerve,  but  from  the  contact  of  the  dissimilar  metals. 
When  two  metals  are  placed  in  contact  with  one  another 
in  the  air,  one  becomes  positive  and  the  other  negative, 
as  we  have  seen  near  the  end  of  Lesson  VII.,  though  the 
charges  are  very  feeble.  Volta,  however,  proved  their 
reality  by  two  different  methods. 

164.  The  Voltaic  Pile.  —  The  second  of  Volta's 
proofs  was  less  direct,  but  even  more  convincing;  and 
consisted  in  showing  that  when  a  num- 
ber of  such  contacts  of  dissimilar  metals 
could  be  arranged  so  as  to  add  their 
electrical  effects  together,  those  effects 
were  more  powerful  in  proportion  to  the 
number  of  the  contacts.  With  this  view 
he  constructed  the  apparatus  known  (in 
honour  of  the  discoverer)  as  the  Voltaic 
Pile  (Fig.  95).  It  is  made  by  placing  a 
pair  of  disks  of  zinc  and  copper  in  contact 
with  one  another,  then  laying  on  the 
copper  disk  a  piece  of  flannel  or  blotting- 
paper  moistened  with  brine,  then  another 
pair  of  disks  of  zinc  and  copper,  and  so  Fig  95 

on,  each  pair  of  disks  in  the  pile  being 
separated  by  a  moist  conductor.    Such  a  pile,  if  composed 
of  a  number  of  such  pairs  of  disks,  will  produce  electricity 


150  ELECTRICITY  AND   MAGNETISM       PART  i 

enough  to  give  quite  a  perceptible  shock,  if  the  top  and 
bottom  disks,  or  wires  connected  with  them,  be  touched 
simultaneously  with  the  moist  fingers.  When  a  single 
pair  of  metals  are  placed  in  contact,  one  becomes  -f  ly 
electrical  to  a  certain  small  extent,  and  the  other  —  ly 
electrical,  or,  in  other  words,  there  is  a  certain  difference  of 
electric  potential  (see  Art.  265)  between  them.  But  when 
a  number  are  thus  set  in  series  with  moist  conductors 
between  the  successive  pairs,  the  difference  of  potential 
between  the  first  zinc  and  the  last  copper  disk  is  increased 
in  proportion  to  the  number  of  pairs ;  for  now  all  the 
successive  small  differences  of  potential  are  added  together. 
165.  The  Crown  of  Cups.  —  Another  combination 
devised  by  Volta  was  his  Couronne  de  Tasses  or  Crown 
of  Cups.  It  consisted  of  a  number  of  cups  (Fig.  96), 
filled  either  with  brine  or  dilute  acid,  into  which  dipped 
a  number  of  compound  strips,  half  zinc,  half  copper, 
the  zinc  portion  of  one  strip  dipping  into  one  cup,  while 


Fig.  96. 

the  copper  portion  dipped  into  the  other  cup.  The 
difference  of  potential  between  the  first  and  last  cups 
is  again  proportional  to  the  number  of  pairs  of  metal 
strips.  This  arrangement,  though  badly  adapted  for 
such  a  purpose,  is  powerful  enough  to  ring  an  electric 
bell,  the  wires  of  which  are  joined  to  the  first  zinc  and 
the  last  copper  strip.  The  electrical  action  of  these 


CHAP.    Ill 


VOLTAIC   CELL 


151 


combinations  is,  however,  best  understood  by  studying 
the  phenomena  of  one  single  cup  or  cell. 

166.  Simple  Voltaic  Cell.  —  Place  in  a  glass  jar 
some  water  having  a  little  sulphuric  acid  or  any  other 
oxidizing  acid  added  to  it  (Fig.  97).  Place  in  it  sep- 
arately two  clean  strips,  one  of  zinc  Z,  and  one  of  copper 
C.  This  cell  is 
capable  of  supply- 
ing a  continuous 
flow  of  electricity 
through  a  wire 
whose  ends  are 
brought  into  con- 
nexion with  the 
two  strips.  When 
the  current  flows 
the  zinc  strip  is 
observed  to  waste 
away ;  its  consump- 
tion in  fact  fur- 
nishes the  energy 
required  to  drive 
the  current  through 
the  cell  and  the 
connecting  wire. 
The  cell  may  therefore  be  regarded  as  a  sort  of  chemical 
furnace  in  which  fuel  is  consumed  to  drive  the  current. 
The  zinc  is  the  fuel,*  the  acid  is  the  aliment,  whilst  the 
copper  is  merely  a  metallic  hand  let  down  into  the  cell 
to  pick  up  the  current,  and  takes  no  part  chemically. 
Before  the  strips  are  connected  by  a  wire  no  appreciable 
difference  of  potential  between  the  copper  and  the  zinc 
will  be  observed  by  an  electrometer ;  because  the  electro- 
meter only  measures  the  potential  at  a  point  in  the  air  or 
oxidizing  medium  outside  the  zinc  or  the  copper,  not  the 

*  Zinc,  as  is  well  known,  will  burn  with  c  blue  flame  in  air  or  oxygen, 
giving  out  heat.     Zinc  foil  is  easily  kindled. 


Fig.  97. 


152  ELECTRICITY  AND   MAGNETISM       PART  i 

potentials  of  the  metals  themselves.  The  zinc  is  trying 
to  dissolve  and  throw  a  current  across  to  the  copper ; 
while  the  copper  is  trying  (less  powerfully)  to  dissolve 
and  throw  a  current  across  the  other  way.  The  zinc 
itself  is  at  about  1-86  volts  higher  potential  than  the 
surrounding  oxidizing  media  (see  Art.  489)  ;  while  the 
copper  is  at  only  about  '81  volts  higher,  having  a  less 
tendency  to  become  oxidized.  There  is  then  a  latent 
difference  of  potential  of  about  1-05  volts  between  the 
zinc  and  the  copper;  but  this  produces  no  current  as 
long  as  there  is  no  metallic  circuit.  If  the  strips  are 
made  to  touch,  or  are  joined  by  a  pair  of  metal  wires, 
immediately  there  is  a  rush  of  electricity  through  the  acid 
from  the  zinc  to  the  copper,  as  indicated  by  the  arrows 
in  Fig.  97,  the  current  returning  by  the  metal  circuit 
from  the  copper  to  the  zinc.  A  small  portion  of  the  zinc 
is  at  the  same  time  dissolved  away;  the  zinc  parting 
with  its  latent  energy  as  its  atoms  combine  with  the  acid. 
This  energy  is  expended  in  forcing  electricity  through 
the  acid  to  the  copper  strip,  and  thence  through  the  wire 
circuit  back  to  the  zinc  strip.  The  copper  strip,  whence 
the  current  starts  on  its  journey  through  the  external 
circuit,  is  called  the  positive  pole,  and  the  zinc  strip  is 
called  the  negative  pole.  If  two  copper  wires  are  united 
to  the  tops  of  the  two  strips,  though  no  current  flows  so 
long  as  the  wires  are  kept  separate,  the  wire  attached  to 
the  zinc  will  be  found  to  be  negative,  and  that  attached 
to  the  copper  positive,  there  being  still  a  tendency  for 
the  zinc  to  oxidize  and  drive  electricity  through  the  cell 
from  zinc  to  copper.  This  state  of  things  is  represented 
by  the  4-  and  —  signs  in  Fig.  97;  and  this  distribution 
of  potentials  led  some  to  consider  the  junction  of  the  zinc 
with  the  copper  wire  as  the  starting  point  of  the  current. 
But  the  real  starting  point  is  in  the  cell  at  the  surface  of 
the  zinc  where  the  chemical  action  is  furnishing  energy ; 
for  from  this  point  there  are  propagated  through  the 
liquid  certain  electro-chemical  actions  (more  fully  ex- 


CHAP,  in  BATTERIES   OF   CELLS  153 

plained  in  Chap.  XI.)  which  have  the  result  of  constantly 
renewing  the  difference  of  potential.  At  the  same  time 
it  will  be  noticed  that  a  few  bubbles  of  hydrogen  gas 
appear  on  the  surface  of  the  copper  plate.  Both  these 
actions  go  on  as  long  as  the  wires  are  joined  to  form  a 
complete  circuit.  The  metallic  zinc  may  be  considered 
as  a  store  of  energy.  We  know  that  if  burned  as  a  fuel 
in  oxygen  or  air  it  will  give  out  that  store  of  energy  as 
heat.  If  burned  in  this  quiet  chemical  manner  in  a 
cell  it  gives  out  its  store  not  as  heat  —  any  heat  in  a  cell 
is  so  much  waste  —  but  in  the  form  of  electric  energy, 
i.e.  the  energy  of  an  electric  current  propelled  by  an 
electromotive  force. 

167.  Effects   produced    by   Current.  —  The    current 
itself  cannot  be  seen  to  flow  through  the  wire  circuit ; 
hence  to  prove  that  any  particular  cell  or  combination 
produces  a  current  requires  a  knowledge  of  some  of  the 
effects  which  currents  can  produce.     These  are  of  various 
kinds.     A  current  flowing  through  a  thin  wire  wTill  heat 
it;  flowing  near  a  magnetic   needle  it  will  cause  it  to 
turn  aside ;   flowing  through  water  and  other  liquids  it 
decomposes  them ;  and,  lastly,  flowing  through  the  living 
body  or  any  sensitive  portion  of  it,  it  produces  certain 
sensations.     These  effects,  thermal,  magnetic,  chemical, 
and  physiological,  will  be  considered  in  special  lessons. 

168.  Voltaic  Battery.  —  If  a  number  of  such  simple 
cells  are  united  in  series,  the  zinc  plate  of  one  joined  to 
the  copper  plate  of  the  next,  and  so  on,  a  greater  differ- 
ence of  potentials  will  be  produced  between  the  copper 
"  pole  "  at  one  end  of  the  series  and  the  zinc  "  pole  "  at 
the  other  end.     Hence,  when  the  two  poles  are  joined 
by  a  wire  there  will  be  a  more  powerful  flow  of  electricity 
than   one    cell  would    cause.     Such    a    combination   of 
Voltaic  Cells  is  called  a  Voltaic  Battery.*     There  are 

*  By  some  writers  the  name  Galvanic  Battery  is  given  in  honour  of 
Galvani ;  but  the  honour  is  certainly  Volta's.  The  electricity  that  flows 
thus  in  currents  is  sometimes  called  Voltaic  Electricity,  or  Galvanic 


164  ELECTRICITY  AND  MAGNETISM        PART  i 

many  ways  of  grouping  a  battery  of  cells,  but  two  need 
special  notice.  If  the  cells  are  joined  up  in  one  row, 
as  in  Fig.  96  or  Fig.  98,  they  are  said  to  be  in  series. 
Electricians  often  represent  a  cell  by  a  symbol  in  which 

a  short  thick  line  stands  for 
I      I     I      I  the  zinc  and  a  longer  thin 

*"•"*'      1 1    II  [I  II       *""*•     line  for  the  copper  (or  car- 
bon).    Thus  Fig.  98  repre- 
Fig.  98.  sents  four    cells   joined  in 

series.     So  joined  they  do 

not  yield  more  current  (more  amperes)  than  a  single  cell 
would  yield,  but  they  yield  that  current  with  a  fourfold 
electromotive  force  (i.e.  with  more  volts  of  pressure). 

The  other  chief  way  of  grouping  cells  is  to  join  all 
the  zincs  together  and  all  the  coppers  (or  carbons)  to- 
gether ;  and  they  are  then 
said  to  be  in  parallel,  or  are     ~»-  > 
joined  "for  quantity."     So 
joined  they  have  no  greater 
electromotive  -  force      than 
one  cell.    The  zincs  act  like  Fi    99 

one  big  zinc,  the  coppers 

like  one  big  copper.  But  they  will  yield  more  current. 
Fig.  99  shows  the  four  cells  grouped  in  parallel;  they 
would  yield  thus  a  current  four  times  as  great  as  one  cell 
alone  would  yield. 

169.  Electromotive-Force.  —  The  term  electromotive- 
force  is  employed  to  denote  that  which  moves  or  tends 
to  move  electricity  from  one  place  to  another.*  For 

Electricity,  or  sometimes  even  Galvanism  (!),  but,  as  we  shall  see,  it  differs 
only  in  degree  from  Frictional  or  any  other  Electricity,  and  both  can  flow 
along  wires,  and  magnetize  iron,  and  decompose  chemical  compounds. 
The  word  Battery  means  an  arrangement  of  one  or  more  cells  ;  just  as  in 
warfare  a  battery  of  guns  means  an  arrangement  of  one  or  more. 

*  The  beginner  must  not  confuse  Electromotive-force,  or  that  which 
tends  to  move  electricity,  with  Electric  "force,"  or  that  force  with  which 
electricity  tends  to  move  matter.  Newton  has  virtually  defined  "force," 
once  for  all,  as  that  which  moves  or  tends  to  move  matter.  When  matter 
is  moved  by  a  magnet  we  speak  rightly  of  magnetic  force  ;  when  electricity 


CHAP,  in  ELECTROMOTIVE   FORCE  155 

brevity  we  sometimes  write  it  E.M.F.  In  this  particular 
case  it  is  obviously  the  result  of  the  difference  of  poten- 
tial, and  proportional  to  it.  Just  as  in  water-pipes  a 
difference  of  level  produces  a  pressure,  and  the  pressure 
produces  a,  flow  so  soon  as  the  tap  is  turned  on,  so  differ- 
ence of  potential  produces  electromotive-force,  and  electro- 
motive-force sets  up  a  current  so  soon  as  a  circuit  is 
completed  for  the  electricity  to  flow  through.  Electro- 
motive-force, therefore,  may  often  be  conveniently  ex- 
pressed as  a  difference  of  potential,  and  vice  versa;  but 
the  student  must  not  forget  the  distinction.  The  unit  in 
which  electromotive-force  is  measured  is  termed  the  volt 
(see  Art.  354).  The  terms  pressure  and  voltage  are  some- 
times used  for  difference  of  potential  or  electromotive-force. 

17O  Volta's  Laws.  —  Volta  showed  (Art.  79)  that 
the  difference  of  potential  between  two  metals  in  contact 
(in  air)  depended  merely  on  what  metals  they  were,  not 
on  their  size,  nor  on  the  amount  of  surface  in  contact. 
He  also  showed  that  when  a  number  of  metals  touched 
one  another  the  difference  of  potential  between  the  first 
and  last  of  the  row  is  the  same  as  if  they  touched  one 
another  directly.  A  quantitative  illustration  from  the 
researches  of  Ayrton  and  Perry  was  given  in  Art.  80. 
But  the  case  of  a  series  of  cells  is  different  from  that  of 
a  mere  row  of  metals  in  contact.  If  in  the  row  of  cells 
the  zincs  and  coppers  are  all  arranged  in  one  order,  so 
that  all  of  them  set  up  electromotive-forces  in  the  same 
direction,  the  total  electromotive-force  of  the  series  will  be 
equal  to  the  electromotive-force  of  one  cell  multiplied  by  the 
number  of  cells. 

Hitherto  we  have  spoken  only  of  zinc  and  copper  as 
the  materials  for  a  cell ;  but  cells  may  be  made  of  any 
two  metals.  The  effective  electromotive-force  of  a  cell 
depends  on  the  difference  between  the  two.  If  zinc  was 

moves  matter  we  may  speak  of  electric  force.  But  E.M.F.  is  quite  a  dif- 
ferent thing-,  not  "  force  "  at  all,  for  it  acts  not  on  matter  but  on  electricity, 
and  tends  to  move  it. 


156  ELECTRICITY  AND   MAGNETISM       PART  i 

used  for  both  metals  in  a  cell  it  would  give  no  current, 
for  each  plate  would  be  trying  to  dissolve  and  to  throw  a 
current  across  to  the  other  with  equal  tendency.  That 
cell  will  have  the  greatest  electromotive-force  or  be  the 
most  "  intense,"  in  which  those  materials  are  used  which 
have  the  greatest  difference  in  their  tendency  to  combine 
chemically  with  the  acid,  or  which  are  widest  apart  on 
the  "  contact-series  "  given  in  Art.  80.  Zinc  and  copper 
are  convenient  in  this  respect ;  and  zinc  and  silver  would 
be  better  but  for  the  expense.  For  more  powerful  bat- 
teries a  zinc-platinum  or  a  zinc-carbon  combination  is 
preferable.  That  plate  or  piece  of  metal  in  a  cell  by 
which  the  current  enters  the  liquid  is  called  the  anode ; 
it  is  that  plate  which  dissolves  away.  The  plate  or  piece 
of  metal  by  which  the  current  leaves  the  cell  is  called  the 
kathode;  it  is  not  dissolved,  and  in  some  cases  receives 
a  deposit  on  its  surface. 

171.  Resistance.  —  The  same  electromotive  -  force 
does  not,  however,  always  produce  a  current  of  the  same 
strength.  The  amount  of  current  depends  not  only  on 
the  force  tending  to  drive  the  electricity  round  the 
circuit,  but  also  on  the  resistance  which  it  has  to 
encounter  and  overcome  in  its  flow.  If  the  cells  be 
partly  choked  with  sand  or  sawdust  (as  is  sometimes 
done  in  so-called  "  Sawdust  Batteries  "  to  prevent  spill- 
ing), or,  if  the  wire  provided  to  complete  the  circuit 
be  very  long  or  very  thin,  the  action  will  be  partly 
stopped,  and  the  current  will  be  weaker,  although  the 
E.M.F.  may  be  unchanged.  The  analogy  of  the  water- 
pipes  will  again  help  us.  The  pressure  which  forces  the 
water  through  pipes  depends  upon  the  difference  of  level 
between  the  cistern  from  which  the  water  flows  and  the 
tap  to  which  it  flows ;  but  the  amount  of  water  that 
runs  through  will  depend  not  on  the  pressure  alone,  but 
on  the  resistance  it  meets  with;  for,  if  the  pipe  be  a 
very  thin  one,  or  choked  with  sand  or  sawdust,  the  water 
will  only  run  slowly  through. 


CHAP,  in  CHEMICAL  ACTIONS  157 

Now  the  metals  in  general  conduct  well :  their  resist- 
ance is  small ;  but  metal  wires  must  not  be  too  thin  or 
too  long,  or  they  will  resist  too  much,  and  permit  only  a 
feeble  current  to  pass  through  them.  The  liquids  in  the 
cell  do  not  conduct  nearly  so  well  as  the  metals,  and  dif- 
ferent liquids  have  different  resistances.  Pure  water  will 
hardly  conduct  at  all,  and  is  for  the  feeble  electricity  of 
the  voltaic  battery  almost  a  perfect  insulator,  though  for 
the  high-potential  electricity  of  the  frictional  machines  it 
is,  as  we  have  seen,  a  fair  conductor.  Salt  and  saltpetre 
dissolved  in  water  are  good  conductors,  and  so  are  dilute 
acids,  though  strong  sulphuric  acid  is  a  bad  conductor. 
The  resistance  of  the  liquid  in  the  cells  may  be  reduced, 
if  desired,  by  using  larger  plates  of  metal  and  putting 
them  nearer  together.  Gases  are  bad  conductors  ;  hence 
the  bubbles  of  hydrogen  gas  which  are  given  off  at  the 
copper  plate  during  the  action  of  the  cell,  and  which  stick 
to  the  surface  of  the  copper  plate,  increase  the  internal 
resistance  of  the  cell  by  diminishing  the  effective  surface 
of  the  plates. 


LESSON  XIV. —  Chemical  Actions  in  the  Cell 

172.  Chemical  Actions.  —  The  production  of  a  cur- 
rent of  electricity  by  a  voltaic  cell  is  always  accompanied 
by  chemical  actions  in  the  cell.  One  of  the  metals  at 
least  must  be  readily  oxidizable,  and  the  liquid  must  be 
one  capable  of  acting  on  the  metal.  As  a  matter  of 
fact,  it  is  found  that  zinc  and  the  other  metals  which 
stand  at  the  electropositive  end  of  the  contact-series  (see 
Art.  80)  are  oxidizable ;  whilst  the  electronegative  sub- 
stances—  copper,  silver,  gold,  platinum,  and  graphite  — 
are  less  oxidizable,  and  the  last  three  resist  the  action  of 
every  single  acid.  There  is  no  proof  that  their  electri- 
cal behaviour  is  due  to  their  chemical  behaviour;  nor 
that  their  chemical  behaviour  is  due  to  their  electrical. 


158  ELECTRICITY  AND   MAGNETISM        PART  i 

Probably  both  result  from  a  common  cause  (see  Art.  80, 
and  also  489).  A  piece  of  quite  pure  zinc  when  dipped 
alone  into  dilute  sulphuric  acid  is  not  attacked  by  the 
liquid.  But  the  ordinary  commercial  zinc  is  not  pure, 
and  when  plunged  into  dilute  sulphuric  acid  dissolves 
away,  a  large  quantity  of  bubbles  of  hydrogen  gas  being 
given  off  from  the  surface  of  the  metal.  Sulphuric  acid 
is  a  complex  substance,  in  which  every  molecule  is  made 
up  of  a  group  of  atoms  —  2  of  Hydrogen,  1  of  Sulphur, 
and  4  of  Oxygen  ;  or,  in  symbols,  H2SO4.  The  chemical 
reaction  by  which  the  zinc  enters  into  combination  with 
the  radical  of  the  acid,  turning  out  the  hydrogen,  is 
expressed  in  the  following  equation:  — 

Zn     +         H2S04  ZnSO4          +         H2 

Zinc     and    Sulphuric  Acid    produce    Sulphate  of  Zinc     and    Hydrogen. 

The  sulphate  of  zinc  produced  in  this  reaction  remains  in 
solution  in  the  liquid. 

Now,  when  a  plate  of  pure  zinc  and  a  plate  of  some 
less-easily  oxidizable  metal  —  copper  or  platinum,  or,  best 
of  all,  carbon  (the  hard  carbon  from  gas  retorts)  —  are 
put  side  by  side  into  the  cell  containing  acid,  no  appre- 
ciable chemical  action  takes  place  until  the  circuit  is  com- 
pleted by  joining  the  two  plates  with  a  wire,  or  by  making 
them  touch  one  another.  Directly  the  circuit  is  com- 
pleted a  current  flows  and  the  chemical  actions  begin, 
the  zinc  dissolving  in  the  acid,  and  the  acid  giving  up  its 
hydrogen  in  streams  of  bubbles.  But  it  will  be  noticed 
that  these  bubbles  of  hydrogen  are  evolved  not  at  the 
zinc  plate,  nor  yet  throughout  the  liquid,  but  at  the  sur- 
face of  the  copper  plate  (or  the  carbon  plate  if  carbon  is 
employed).  This  apparent  transfer  of  the  hydrogen 
gas  through  the  liquid  from  the  surface  of  the  zinc  plate 
to  the  surface  of  the  copper  plate  where  it  appears  is  very 
remarkable.  The  ingenious  theory  framed  by  Grotthuss 
to  account  for  it,  is  explained  in  Lesson  XL VII.  on 
Electro-Chemistry. 


CHAP,  in       LOCAL   CHEMICAL  ACTIONS  159 

These  chemical  actions  go  on  as  long  as  the  current 
passes.  The  quantity  of  zinc  used  up  in  each  cell  is  pro- 
portional to  the  amount  of  electricity  which  flows  round 
the  circuit  while  the  battery  is  at  work;  or,  in  other 
words,  is  proportional  to  the  current.  The  quantity  of 
hydrogen  gas  evolved  is  also  proportional  to  the  amount 
of  zinc  consumed,  and  also  to  the  current.  After  the 
acid  has  thus  dissolved  zinc  in  it,  it  will  no  longer  act 
as  a  corrosive  solvent ;  it  has  been  "  killed,"  as  workmen 
say,  for  it  has  been  turned  into  sulphate  of  zinc.  The 
battery  will  cease  to  act,  therefore,  either  when  the  zinc 
has  all  dissolved  away,  or  when  the  acid  has  become 
exhausted,  that  is  to  say,  when  it  is  all  turned  into  sul- 
phate of  zinc.  Stout  zinc  plates  will  last  a  long  time, 
but  the  acids  require  to  be  renewed  frequently,  the  spent 
liquor  being  emptied  out. 

173.  Local  Action.  —  When  the  circuit  is  not  closed 
the  current  cannot  flow,  and  there  should  be  no  chemical 
action  so  long  as  the  battery  is  producing  no  current. 
The  impure   zinc   of  commerce,  however,  does   not  re- 
main quiescent  in  the  acid,  but  is  continually  dissolving 
and   giving  off   hydrogen  bubbles.     This  local  action, 
as  it  is  termed,  is  explained  in  the  following  manner  :  — 
The  impurities  in  the  zinc  consist  of  particles  of  iron, 
arsenic,  and  other  metals.     Suppose  a  particle  of  iron  to 
be  on  the  surface  anywhere  and  in  contact  with  the  acid. 
It  will  behave  like  the  copper  plate  of  a  battery  towards 
the  zinc  particles  in  its  neighbourhood,  for  a  local  differ- 
ence of  potential  will  be  set  up  at  the  point  where  there 
is  metallic  contact,  causing  a  local  or  parasitic  current  to 
run  from  the  particles  of  zinc  through  the  acid  to  the 
particle  of  iron,  arid  so  there  will  be  a  continual  wasting 
of  the  zinc,  both  when  the  battery  circuit  is  closed  and 
when  it  is  open. 

174.  Amalgamation  of  Zinc.  —  We  see  now  why  a 
piece  of  ordinary  commerical  zinc  is  attacked  on  being 
placed  in  acid.     There  is  local  action  set  up  all  over  its 


160  ELECTRICITY  AND   MAGNETISM        PART  i 

surface  in  consequence  of  the  metallic  impurities  in  it. 
To  do  away  with  this  local  action,  and  abolish  the 
wasting  of  the  zinc  while  the  battery  is  at  rest,  it  is 
usual  to  amalgamate  the  surface  of  the  zinc  plates  with 
mercury.  The  surface  to  be  amalgamated  should  be 
cleaned  by  dipping  into  acid,  and  then  a  few  drops  of 
mercury  should  be  poured  over  the  surface  and  rubbed 
into  it  with  a  bit  of  linen  rag  tied  to  a  stick.  The 
mercury  unites  with  the  zinc  at  the  surface,  forming  a 
pasty  amalgam.  The  iron  particles  do  not  dissolve  in 
the  mercury,  but  float  up  to  the  surface,  whence  the 
hydrogen  bubbles  which  may  form  speedily  carry  them 
off.  As  the  zinc  in  this  pasty  amalgam  dissolves  into 
the  acid  the  film  of  mercury  unites  with  fresh  portions 
of  zinc,  and  so  presents  always  a  clean  bright  surface  to 
the  liquid. 

A  newer  and  better  process  is  to  add  about  4  per  cent 
of  mercury  to  the  molten  zinc  before  casting  into  plates 
or  rods.  If  the  zinc  plates  of  a  battery  are  well  amal- 
gamated there  should  be  no  evolution  of  hydrogen  bub- 
bles when  the  circuit  is  open.  Nevertheless  there  is  still 
always  a  little  wasteful  local  action  during  the  action  of 
the  battery.  Jacobi  found  that  while  one  part  of  hydro- 
gen was  devolved  at  the  kathode,  33-6  parts  of  zinc  were 
dissolved  at  the  anode,  instead  of  the  32-5  parts  which 
are  the  chemical  equivalent  of  the  hydrogen. 

175.  Polarization.  —  The  bubbles  of  hydrogen  gas 
liberated  at  the  surface  of  the  copper  plate  stick  to  it  in 
great  numbers,  and  form  a  film  over  its  surface;  hence 
the  effective  amount  of  surface  of  the  copper  plate  is 
very  seriously  reduced  in  a  short  time.  When  a  simple 
cell,  or  battery  of  such  cells,  is  set  to  produce  a  current, 
it  is  found  that  the  current  after  a  few  minutes,  or  even 
seconds,  falls  off  very  greatly,  and  may  even  be  almost 
stopped.  This  immediate  falling  off  in  the  current, 
which  can  be  observed  with  any  galvanometer  and  a 
pair  of  zinc  and  copper  plates  dipping  into  acid,  is 


CHAP.    Ill 


POLARIZATION  IN   CELLS  1G1 


almost  entirely  due  to  the  film  of  hydrogen  bubbles 
sticking  to  the  copper  pole.  A  battery  which  is  in  this 
condition  is  said  to  be  "  polarized." 

176.  Effects  of  Polarization.  —  The  film  of  hydrogen 
bubbles  affects  the  strength  of  the  current  of  the  cell  in 
two  ways. 

Firstly,  it  weakens  the  current  by  the  increased  resist- 
ance which  it  offers  to  the  flow,  for  bubbles  of  gas  are  bad 
conductors ;  and,  worse  than  this, 

Secondly,  it  weakens  the  current  by  setting  up  an 
opposing  electromotive-force;  for  hydrogen  is  almost  as 
oxidizable  a  substance  as  zinc,  especially  when  it  is  being 
deposited  (or  in  a  "  nascent "  state),  and  is  electropositive, 
standing  high  in  the  series  on  p.  85.  Hence  the  hydro- 
gen itself  produces  a  difference  of  potential,  which  would 
tend  to  start  a  current  in  the  opposite  direction  to  the 
true  zinc-to-copper  current.  No  cell  in  which  the  polari- 
zation causes  a  rapid  falling  off  in  power  can  be  used  for 
closed  circuit  work. 

It  is  therefore  a  very  important  matter  to  abolish  this 
polarization,  otherwise  the  currents  furnished  by  batteries 
would  not  be  constant. 

177.  Remedies  against  Internal  Polarization.  —  Vari- 
ous remedies  have  been  practised  to  reduce  or  prevent 
the  polarization  of  cells.      These    may  be    classed   as 
mechanical,  chemical,  and  electrochemical. 

1.  Mechanical  Means.  —  If  the  hydrogen  bubbles  be 
simply  brushed  away  from  the  surface  of  the  kathode, 
the  resistance  they  caused  will  be  diminished.  If  air 
be  blown  into  the  acid  solution  through  a  tube,  or  if 
the  liquid  be  agitated  or  kept  in  constant  circulation  by 
siphons,  the  resistance  is  also  diminished.  If  the  surface 
be  rough  or  covered  with  points,  the  bubbles  collect  more 
freely  at  the  points  and  are  quickly  carried  up  to  the 
surface,  and  so  got  rid  of.  This  remedy  was  applied  in 
Smee's  Cell,  which  consisted  of  a  zinc  and  a  platinized 
silver  plate  dipping  into  dilute  sulphuric  acid  ;  the  silver 


162  ELECTRICITY   AND   MAGNETISM        PART  i 

plate,  having  its  surface  thus  covered  with  a  rough  coat- 
ing of  finely  divided  platinum,  gave  up  the  hydrogen 
bubbles  freely ;  nevertheless,  in  a  battery  of  Smee  Cells 
the  current  diminishes  greatly  after  a  few  minutes. 

2.  Chemical  Means.  —  If  a  highly-oxidizing  substance 
be  added  to  the  acid  it  will  destroy  the  hydrogen  bubbles 
whilst  they  are  still  in  the  nascent  state,  and  thus  will 
prevent  both  the  increased  internal  resistance  and  the 
opposing   electromotive-force.      Such  substances  are  bi- 
chromate of  potash,  nitric  acid,  and  chlorine. 

3.  Electrochemical  Means.  —  It  is  possible  by  employ- 
ing double  cells,  as  explained  in  the  next  lesson,  to  so 
arrange  matters  that  some  solid  metal,  such  as  copper, 
shall  be  liberated   instead  of  hydrogen  bubbles,  at  the 
point  where  the  current  leaves  the  liquid.     This  electro- 
chemical exchange  entirely  obviates  polarization. 

178.  Simple  Laws  of  Chemical  Action  in  the  Cell.  — 
We  will  conclude  this  section  by  enumerating  the  two 
simple  laws  of  chemical  action  in  the  cell. 

I.  The  amount  of  chemical  action  in  the  cell  is  propor- 
tional to  the  quantity  of  electricity  that  passes  through  it  — 
that   is  to  say,  is  proportional  to   the  current  while  it 
passes. 

A  current  of  one  ampere  flowing  through  the  cell  for 
one  second  causes  0-00033698  (or  ^Vr)  of  a  gramme  of 
zinc  to  dissolve  in  the  acid,  and  liberates  0-000010384 
(or  ^3-^2)  of  a  gramme  of  hydrogen. 

II.  The  amount  of  chemical  action  is  equal  in  each  cell 
of  a  battery  consisting  of  cells  joined  in  series. 

The  first  of  these  laws  was  thought  by  Faraday,  who 
discovered  it,  to  disprove  Volta's  contact  theory.  He 
foresaw  that  the  principle  of  the  conservation  of  energy 
would  preclude  a  mere  contact  force  from  furnishing  a 
continuous  supply  of  current,  and  hence  ascribed  the 
current  to  the  chemical  actions  which  were  proportional 
in  quantity  to  it.  How  the  views  of  Volta  and  Faraday 
are  to  be  harmonized  has  been  indicated  in  the  last 


CHAP,  in  VOLTAIC   CELLS  163 

paragraph  of  Art.  80.  These  laws  only  relate  to  the 
useful  chemical  action,  and  do  not  include  the  waste  of 
"local"  actions  (Art.  166)  due  to  parasitic  currents  set 
up  by  impurities. 

LESSON  XV.  —  Voltaic  Cells 

179.  A  good  Voltaic  Cell  should  fulfil  all  or  most  of 
the  following  conditions  :  — 

1.  Its  electromotive-force  should  be  high  and  con- 

stant. 

2.  Its  internal  resistance  should  be  small. 

3.  It  should  give  a  constant  current,  and  therefore 

must  be  free  from  polarization,  and  not  liable 
to  rapid  exhaustion,  requiring  frequent  renewal 
of  the  acid. 

4.  It  should  be  perfectly  quiescent  when  the  circuit 

is  open. 

5.  It  should  be  cheap  and  of  durable  materials. 

6.  It  should  be  manageable,  and  if  possible,  should 

not  emit  corrosive  fumes. 

No  single  cell  fulfils  all  these  conditions,  however, 
and  some  cells  are  better  for  one  purpose  and  some  for 
another.  Thus,  for  telegraphing  through  a  long  line  of 
wire  a  considerable  internal  resistance  in  the  battery  is 
no  great  disadvantage ;  while,  for  producing  an  electric 
light,  much  internal  resistance  is  absolutely  fatal.  The 
electromotive-force  of  a  battery  depends  on  the  materials 
of  the  cell,  and  on  the  number  of  cells  linked  together, 
and  a  high  E.M.F.  can  therefore  be  gained  by  choosing 
the  right  substances  and  by  taking  a  large  number  of 
cells.  The  resistance  within  the  cell  can  be  diminished 
by  increasing  the  size  of  the  plates,  by  bringing  them 
near  together,  so  that  the  thickness  of  the  liquid  between 
them  may  be  as  small  as  possible,  and  by  choosing  liquids 
that  are  good  conductors. 


164  ELECTRICITY   AND   MAGNETISM       PART  i 

180.  Classification  of  Cells. — Of  the  innumerable 
forms  of  cells  that  have  been  invented,  only  those  of  first 
importance  can  be  described.  Cells  are  sometimes  classi- 
fied into  two  groups,  according  as  they  contain  one  or 
two  fluids,  or  electrolytes,  but  a  better  classification  is 
that  adopted  in  Art.  177,  depending  on  the  means  of  pre- 
venting polarization. 

CLASS  I.  —  WITH  MECHANICAL  DEPOLARIZATION. 
(Single  Fluid.) 

The  simple  cell  of  Yolta,  with  its  zinc  and  copper 
plates,  has  been  already  described.  The  larger  the  cop- 
per plate,  the  longer  time  does  it  take  to  polarize.  Cruick- 
shank  suggested  to  place  the  plates  vertically  in  a  trough, 
producing  a  more  powerful  combination.  Dr.  Wollaston 
proposed  to  use  a  plate  of  copper  of  double  size,  bent 
round  so  as  to  approach  the  zinc  on  both  sides,  thus 
diminishing  the  resistance,  and  allowing  the  hydrogen 
more  surface  to  deposit  upon.  Smee,  as  we  have  seen, 
replaced  the  copper  plate  by  platinized  silver,  and  Walker 
suggested  the  use  of  plates  of  hard  carbon  instead  of  cop- 
per or  silver,  thereby  saving  cost,  and  at  the  same  time 
increasing  the  electromotive-force.  The  roughness  of  the 
surface  facilitates  the  escape  of  hydrogen  bubbles.  By 
agitating  such  cells,  or  raising  their  kathode  plates  for  a 
few  moments  into  the  air,  their  power  is  partially  restored. 
The  Law  cell,  used  in  the  United  States  for  open-circuit 
work,  is  of  this  class :  it  has  a  small  rod  of  zinc  and  a 
cleft  cylinder  of  carbon  of  large  surface  immersed  in 
solution  of  salammoniac. 

CLASS  II.  —  WITH  CHEMICAL  DEPOLARIZATION. 

In  these  cells,  in  addition  to  the  dilute  acid  or  other 
excitant  to  dissolve  the  zinc,  there  is  added  some  more 


CHAP,  in    EXCITANTS  AND  DEPOLARIZERS          165 


powerful  chemical  agent  as  a  depolarizer.  Amongst  de- 
polarizers the  following  are  chiefly  used  :  —  Nitric  acid, 
solutions  of  chromic  acid,  of  bichromate  of  potash,  of 
bichromate  of  soda,  of  nitrate  of  potash,  or  of  ferric 
chloride;  chlorine,  bromine,  black  oxide  of  manganese, 
sulphur,  peroxide  of  lead,  red  lead,  oxide  of  copper. 
Most  of  these  materials  would,  however,  attack  the 
copper  as  well  as  the  zinc  if  used  in  a  zinc-copper  cell. 
Hence  they  can  only 
be  made  use  of  in  zinc- 
carbon  or  zinc-plati- 
num cells.  Nitric  acid 
also  attacks  zinc  when 
the  circuit  is  open. 
Hence  it  cannot  be  em- 
ployed in  the  same  sin- 
gle cell  with  the  zinc 
plate.  In  the  Bichro- 
mate Cell,  invented  by 
Poggendorff,  bichro- 
mate of  potash  is  added 
to  the  sulphuric  acid. 

• 


Fig.  100. 


This  cell  is  most  con- 
veniently made  up  as 
shown  in  Fig.  100,  in 
which  a  plate  of  zinc  is 
the  anode,  and  a  pair 
of  carbon  plates,  one  on  each  side  of  the  zinc,  joined 
together  at  the  top  serve  as  a  kathode.  As  this  solution 
would  attack  the  zinc  even  when  the  circuit  is  open,  the 
zinc  plate  is  fixed  to  a  rod  by  which  it  can  be  drawn  up 
out  of  the  solution  when  the  cell  is  not  being  worked. 

To  obviate  the  necessity  of  this  operation  the  device 
is  adopted  of  separating  the  depolarizer  from  the  liquid 
into  which  the  zinc  dips.  In  the  case  of  liquid  depola- 
rizers this  is  done  by  the  use  of  an  internal  porous  cell  or 
partition.  Porous  cells  of  earthenware  or  of  parchment 


166  ELECTRICITY  AND   MAGNETISM       PART  i 

paper  allow  the  electric  current  to  flow  while  keeping  the 
liquids  apart.  In  one  compartment  is  the  zinc  anode 
dipping  into  its  aliment  of  dilute  acid :  in  the  other  com- 
partment the  carbon  (or  platinum)  kathode  dipping  into 
the  depolarizer.  Such  cells  are  termed  two-fluid  cells. 
In  the  case  of  solid  depolarizers  such  as  black  oxide  of 
manganese,  oxide  of  copper,  etc.,  the  material  merely 
needs  to  be  held  up  to  the  kathode.  All  solid  depola- 
rizers are  slow  in  acting. 

CLASS  III.  —  WITH    ELECTROCHEMICAL   DEPOLARIZA- 
TION. 

When  any  soluble  metal  is  immersed  in  a  solution  of 
its  own  salt  —  for  example,  zinc  dipped  into  sulphate  of 
zinc,  or  copper  into  sulphate  of  copper  —  there  is  a  defi- 
nite electromotive-force  between  it  and  its  solution,  the 
measure  of  its  tendency  to  dissolve.  If  a  current  is  sent 
from  metal  to  solution  some  of  the  metal  dissolves ;  if, 
however,  the  current  is  sent  from  solution  to  metal  some 
more  metal  will  be  deposited  (or  "  plated  ")  out  of  the 
solution.  But  as  long  as  the  chemical  nature  of  the 
surface  and  of  the  liquid  is  unchanged  there  will  be  no 
change  in  the  electromotive-force  at  the  surface.  It 
follows  that  if  a  cell  were  made  with  two  metals,  each 
dipping  into  a  solution  of  its  own  salt,  the  two  solutions 
being  kept  apart  by  a  porous  partition,  such  a  cell  would 
never  change  its  electromotive-force.  The  anode  would 
not  polarize  where  it  dissolves  into  the  excitant ;  the 
kathode  would  not  polarize,  since  it  receives  merely  an 
additional  thickness  of  the  same  sort  as  itself.  This 
electrochemical  method  of  avoiding  polarization  was  dis- 
covered by  Daniell.  It  is  the  principle  not  only  of  the 
Daniell  cell,  but  of  the  Clark  cell  and  of  others.  For  per- 
fect constancy  the  two  salts  used  should  be  salts  of  the 
same  acid,  both  sulphates,  or  both  chlorides,  for  example. 

181.   Daniell's    Cell. —Each    cell    or   "element"   of 


CHAP.    Ill 


DANIELL'S   CELL 


167 


DauielPs  battery  has  an  inner  porous  cell  or  partition  to 
keep  the  separate  liquids  from  mixing.  The  outer  cell 
(Fig.  101)  is  usually  of  copper,  and  serves  also  as  a 
copper  kathode.  Within  it  is  placed  a  cylindrical  cell  of 
un glazed  porous  ware  (a  cell  of  parchment,  or  even  of 
brown  paper,  will  answer),  and  in  this  is  a  rod  of  amalga- 
mated zinc  as  anode.  The  liquid 
in  the  inner  cell  is  dilute  sulphuric 
acid  or  dilute  sulphate  of  zinc ; 
that  in  the  outer  cell  is  a  saturated 
solution  of  sulphate  of  copper 
("blue  vitriol"),  some  spare 
crystals  of  the  same  substance 
being  contained  in  a  perforated 
shelf  at  the  top  of  the  cell,  in 
order  that  they  may  dissolve  and 
replace  that  which  is  used  up 
while  the  battery  is  in  action. 

When  the  circuit  is  closed  the  zinc  dissolves  in  the 
dilute  acid,  forming  sulphate  of  zinc,  and  liberating 
hydrogen ;  but  this  gas  does  not  appear  in  bubbles  on 
the  surface  of  the  copper  cell,  for,  since  the  inner  cell  is 
porous,  the  molecular  actions  (by  which  the  freed  atoms 
of  hydrogen  are,  as  explained  by  Fig.  266,  handed  on 
through  the  acid)  traverse  the  pores  of  the  inner  cell,  and 
there,  in  the  solution  of  sulphate  of  copper,  the  hydrogen 
atoms  are  exchanged  for  copper  atoms,  the  result  being 
that  pure  copper,  and  not  hydrogen  gas,  is  deposited  on 
the  outer  copper  plate.  Chemically  these  actions  may  be 
represented  as  taking  place  in  two  stages. 

Zn        +       H2SO4  ZnSO4        +        H2 

Zinc    and  Sulphuric  Acid    produce    Sulphate  of  Zinc  and  Hydrogen. 

And  then 


II. 


CuSO4 


H2S04 


Cu. 


Hydrogen  and  Sulphate  of  Copper  produce  Sulphuric  Acid  and     Copper. 


168  ELECTRICITY  AND   MAGNETISM       PART  i 

The  hydrogen  is,  as  it  were,  translated  electro- 
chemically  into  copper  during]  the  round  of  changes, 
and  so  while  the  zinc  dissolves  away  the  copper  grows, 
the  dilute  sulphuric  acid  gradually  changing  into  sul- 
phate of  zinc,  and  the  sulphate  of  copper  into  sulphuric 
acid.  In  the  case  in  which  a  solution  of  sulphate  of  zinc 
is  used  there  is  no  need  to  consider  any  hydrogen  atoms, 
copper  being  exchanged  chemically  for  zinc.  There  is 
therefore  no  polarization  so  long  as  the  copper  solution  is 
saturated ;  and  the  cell  is  very  constant,  though  not  so 
constant  in  all  cases  as  Clark's  standard  cell  described  in 
Art.  188,  owing  to  slight  variations  in  the  electromotive- 
force  as  the  composition  of  the  other  fluid  varies.  When 
sulphuric  acid  diluted  with  twelve  parts  of  water  is  used 
the  E.M.F.  is  1-178  volts.  The  E.M.F.  is  1-07  volts  when 
concentrated  zinc  sulphate  is  used ;  1-1  volts  when  a  half- 
concentrated  solution  of  zinc  sulphate  is  used ;  and,  in 
the  common  cells  made  up  with  water  or  dilute  acid, 
1-1  volts  or  less.  Owing  to  its  constancy,  this  battery, 
made  up  in  a  convenient  flat  form  (Fig.  106),  has  been 
much  used  in  telegraphy.  It  is  indispensable  in  those 
"closed  circuit"  methods  of  telegraphy  (Art.  500),  where 
the  current  is  kept  always  flowing  until  interrupted  by 
signalling. 

182.  Grove's  Cell. —  Sir  William  Grove  devised  a 
form  of  cell  having  both  higher  voltage  and  smaller 
internal  resistance  than  DanielFs  cell.  In  Grove's  ele- 
ment there  is  an  outer  cell  of  glazed  ware  or  of  ebonite, 
containing  the  amalgamated  zinc  plate  and  dilute  sul- 
phuric acid.  In  the  inner  porous  cell  a  piece  of  platinum 
foil  serves  as  the  negative  pole,  and  it  dips  into  the 
strongest  nitric  acid.  There  is  no  polarization  in  this 
cell,  for  the  hydrogen  liberated  by  the  solution  of  the 
zinc  in  dilute  sulphuric  acid,  in  passing  through  the 
nitric  acid  in  order  to  appear  at  the  platinum  pole,  de- 
composes the  nitric  acid  and  is  itself  oxidized,  producing 
water  and  the  red  fumes  of  nitric  peroxide  gas.  This 


CHAP,  in  GROVE'S   CELL  169 

gas  does  not,  however,  produce  polarization,  for  as  it  is 
very  soluble  in  nitric  acid,  it  does  not  form  a  film  upon 
the  face  of  the  platinum  plate,  nor  does  it,  like  hydrogen, 
set  up  an  opposing  electromotive-force  with  the  zinc. 
The  Grove  cells  may  be  made  of  a  flat  shape,  the  zinc 
being  bent  up  so  as  to  embrace  the  flat  porous  cell  on 
both  sides.  This  reduces  the  internal  resistance,  which 
is  already  small  on  account  of  the  good  conducting 
powers  of  nitric  acid.  Hence  the  Grove  cell  will  furnish 
for  three  or  four  hours  continuously  a  strong  current. 
The  E.M.F.  of  one  cell  is  about  1-9  volts,  and  its  internal 
resistance  is  very  low  (about  0-1  ohm  for  the  quart  size). 
A  single  cell  will  readily  raise  to  a  bright  red  heat  two 
or  three  inches  of  thin  platinum  wire,  or  drive  a  small 
electromagnetic  engine.  For  producing  larger  power  a 
number  of  cells  must  be  joined  up  in  series,  the  plat- 
inum of  one  cell  being  clamped  to  the  zinc  of  the  next 
to  it.  Fifty  such  cells,  each  holding  about  a  quart  of 
liquid,  amply  suffice  to  produce  an  electric  arc  light,  as 
will  be  explained  in  Lesson  XXXIX. 

183.  Bunsen's  Cell.  —  T lie  cell  which  bears  Bunsen's 
name  is  a  modification  of  that  of  Grove,  and  was  indeed 
originally  suggested  by  him.  In  the  Bunsen  cell  the 
expensive  *  platinum  foil  is  replaced  by  a  rod  or  slab  of 
hard  gas  carbon.  A  cylindrical  form  of  cell,  with  a  rod 
of  carbon,  is  shown  in  Fig.  102.  The  voltage  for  a  zinc- 
carbon  combination  is  a  little  higher  than  for  a  zinc- 
platinum  one,  which  is  an  advantage  ;  but  the  Bunsen 
cell  is  troublesome  to  keep  in  order,  and  there  is  some 
difficulty  in  making  a  good  contact  between  the  rough 
surface  of  the  carbon  and  the  copper  strap  which  connects 

*  Platinum  costs  about  30  shillings  an  ounce  — nearly  half  as  much  as 
gold  ;  while  a  hundredweight  of  the  gas  carbon  may  be  had  for  a  mere  trifle, 
often  for  nothing  more  than  the  cost  of  carrying  it  from  the  gasworks.  An 
artificial  carbon  prepared  by  grinding  up  gas  carbon  with  some  carbonaceous 
matter  such  as  tar,  sugar  residues,  etc.,  then  pressing  into  moulds,  and 
baking  in  a  furnace,  is  used  both  for  battery  plates  and  for  the  carbon  rods 
used  in  arc  lamps. 


170 


ELECTRICITY  AND   MAGNETISM       PART  i 


the  carbon  of  one  cell  to  the  zinc  of  the  next.  The  top 
part  of  the  carbon  is  sometimes 
impregnated  with  paraffin  wax  to 
keep  the  acid  from  creeping  np, 
and  electrotyped  with  copper. 
Fig.  103  shows  the  usual  way  of 
coupling  up  a  series  of  five  such 
cells.  The  Bunsen's  battery  will 
continue  to  furnish  a  current  for 
a  longer  time  than  the  flat  Grove's 
cells,  on  account  of  the  larger 
quantity  of  acid  contained  by  the 
cylindrical  pots.* 

Chromic  solutions,  formed  by 
adding  strong  sulphuric  acid  to 
solutions  of  bichromate  of  potash  or  of  soda,  are  often 
used  instead  of  nitric  acid,  in  cells  of  this  form.  Soluble 


Fig.  102. 


Fif,*.  103. 

depolarizers  in  the  form  of  chromic  powders  are  made 
by  heating  strong  sulphuric  acid  and  gradually  stirring 
into  it  powdered  bichromate  of  soda.  The  pasty  mass  is 
then  cooled  and  powdered. 

*  Callan  constructed  a  large  battery  in  which  cast-iron  formed  the 
positive  pole,  being  immersed  in  strong  nitric  acid,  the  zincs  dipping  into 
dilute  acid.  The  iron  under  these  circumstances  is  not  acted  upon  by  the 
acid,  but  assumes  a  so-called  "  passive  state."  In  this  condition  its  surface 
appears  to  be  impregnated  with  a  film  of  magnetic  peroxide,  or  of  oxygen. 


CHAP.    Ill 


LECLANCHE'S   CELL 


171 


184.  Leclanche's  Cell.  —  For  working  electric  bells 
and  telephones,  and  also  to  a  limited  extent  in  teleg- 
raphy, a  zinc-carbon  cell  is  employed,  invented  by  Le- 
clanche,  in  which  the  exciting  liquid  is  not  dilute  acid,  but 
a  solution  of  salammoniac.  In  this  the  zinc  dissolves, 
forming  a  double  chloride  of  zinc  and  ammonia,  while 
ammonia  gas  and  hydrogen  are  liberated  at  the  carbon 
pole.  The  depolarizer  is  the  black  binoxide  of  manga- 
nese, fragments  of  which,  mixed  with  powdered  carbon, 
are  held  up  to  the  carbon  kathode  either  by  packing  them 
together  inside  a  porous  pot  or  by  being  attached  as  an 
agglomerated  block.  The  oxide  of  manganese  will  slowly 


Fig.  104. 

yield  up  oxygen  as  required.  If  used  to  give  a  continuous 
current  for  many  minutes  together,  the  power  of  this  cell 
falls  off  owing  to  the  accumulation  of  the  hydrogen  bub- 
bles ;  but  if  left  to  itself  for  a  time  the  cell  recovers  itself, 
the  binoxide  gradually  destroying  the  polarization.  As 
the  cell  is  in  other  respects  perfectly  constant,  and  does 
not  require  renewing  for  months  or  years,  it  is  well  adapted 
for  domestic  purposes.  It  has  the  advantage  of  not  con- 
taining corrosive  acids.  Millions  of  these  cells  are  in  use 
on  "  open-circuit "  service  —  that  is  to  say,  for  those  cases 
in  which  the  current  is  only  required  for  a  few  moments 
at  a  time,  and  the  circuit  usually  left  open.  Three 
Leclanche  cells  are  shown  joined  in  series,  in  Fig.  104. 


172  ELECTRICITY   AND   MAGNETISM       PART  i 

Walker  used  sulphur  in  place  of  oxide  of  manganese. 
Niaudet  employed  bleaching  powder  (so  called  chloride 
of  lime)  as  depolarizer,  it  being  rich  in  chlorine  and  oxy- 
gen. Common  salt  may  be  used  instead  of  salammoniac. 
Modifications  of  the  Leclanche  cell  in  which  the 
excitant  cannot  be  spilled  are  used  for  portability.  The 
space  inside  the  cell  is  filled  up  with  a  spongy  or  gelati- 
nous mass,  or  even  with  plaster  of  Paris,  in  the  pores  of 
which  the  salammoniac  solution  remains.  They  are 
known  as  dry  cells. 

185.  Lalande's  Cell.  — This  cell  belongs  to  Class  II., 
having  as  depolarizer  oxide  of  copper  mechanically  at- 
tached to  a  kathode  of  copper  or  iron.     The  anode  is 
zinc,  and  the  exciting  liquid  is  a  30  per  cent  solution  of 
caustic  potash  into  which   the   zinc   dissolves  (forming 
zincate  of  potash),  whilst  metallic  copper  is  reduced  in  a 
granular  state  at  the  kathode.     It  has  only  0-8  to  0-9 
volts  of  E.M.F.,  but  is  capable  of  yielding  a  large  and 
constant  current. 

186.  De  la  Rue's  Battery.  —  De  la  Rue  constructed 
a  constant  cell  belonging  to  Class  III.,  in  which  zinc  and 
silver  are  the  two  metals,  the  zinc  being  immersed  in 
chloride  of  zinc,  and  the  silver  embedded  in  a  stick  of 
fused  chloride   of  silver.     As  the  zinc  dissolves  away, 
metallic  silver  is  deposited  upon  the  kathode,  just  as  the 
copper  is  in  the  DanielPs  cell.     De  la  Rue  constructed 
an  enormous  battery  of   over  11,000  little  cells.      The 
difference  of  potential  between  the  first  zinc   and   last 
silver    of     this    battery    was     over     11,000    volts,    yet 
even   so  no   spark   would  jump  from  the  +   to  the   — 
pole    until   they  were   brought   to   within   less  than   a 
quarter   of   an  inch   of  one  another.     With   8040  cells 
the    length    of    spark  was    only  0-08    of    an    inch,   or 
0-2  cm. 

187.  Gravity  Cells.  —  Instead  of  employing  a  porous 
cell  to  keep  the  two  liquids  separate,  it  is  possible,  where 
one  of  the  liquids  is  heavier  than  the  other,  to  arrange 


CHAP,  in         CLARK'S   STANDARD   CELL 


173 


that  the  heavier  liquid  shall  form  a  stratum  at  the 
bottom  of  the  cell,  the  lighter  floating  upon  it.  Such 
arrangements  are  called  gravity  cells ;  but  the  separation 
is  never  perfect,  the  heavy  liquid  slowly  diffusing  up- 
wards. Daniell's  cells  arranged  as  gravity  cells  have 
been  contrived  by  Meidinger,  Minotto,  Callaud,  and  Lord 
Kelvin.  In  Siemens'  modification  paper-pulp  is  used 
to  separate  the  two  liquids.  The  "  Sawdust  Battery  " 
of  Kelvin  is  a  Daniell's  battery,  having  the  cells  filled 
with  sawdust,  to  prevent  spilling  and  make  them 
portable. 

188.  Clark's  Standard  Cell.  —  A  standard  cell  whose 
E.M.F.  is  even  more  constant  than  that  of  the  Daniell 
was  suggested  by  Latimer 
Clark.  This  cell,  which  is 
now  adopted  as  the  inter- 
national standard  cell,  con- 
sists of  an  anode  of  pure 
zinc  in  a  concentrated  solu- 
tion of  zinc-sulphate,  whilst 
the  kathode  is  of  pure  mer- 
cury in  contact  with  a  paste 
of  mercurous  sulphate.  Pre- 


n\^.Glass  tube 


Cement 


—Cork 


Air-bubble 
-Zinc  sulphate 
—  Crystals 


Paste 


Mercury 


Platinum  wire 


Fig.  105. 

Its  E.M.F.  is  1434  volts  at 


cise  instructions  for  setting 
up  Clark  cells  are  given 
in  Appendix  B  at  the  end 
of  this  book.  Fig.  105 
shows,  in  actual  size,  the 
form  of  the  Clark  cell. 
15°  C. 

Weston  uses  a  cadmium  anode  immersed  in  sulphate 
of  cadmium  and  finds  the  cell  so  modified  to  give  1-025 
volts  at  all  ordinary  temperatures. 

Von  Helmholtz  has  used  mercurous  chloride  (calomel) 
and  chloride  of  zinc,  in  place  of  sulphates,  in  a  standard 
cell.  Carhart  finds  its  E.M.F.  (a  little  over  1  volt)  to 
vary  with  the  dilution  of  the  chloride  of  zinc. 


174 


ELECTRICITY   AND    MAGNETISM       PART  i 


189.  Statistics  of  Cells.  —  The  following  table  gives 
the  electromotive-forces  of  the  various  batteries  enu- 
merated :  — 


Name. 

Anode. 

Excitant. 

Depolarizer. 

Kathode. 

Approxi- 
mate 
Volts. 

Class  I. 

(Solution  of) 

Volta   (Wollaston, 

Zinc 

H2S04 

none 

Copper 

1-0  to  0-5 

etc.)    . 

Smee      . 

Zinc 

H2S04 

none 

Platinized 

1-0  to  0-5 

Silver 

Law        . 

Zinc 

H2S04 

none 

Carbon 

l'OtoO'5 

Class  II. 

Poggendorff  (Gre- 

Zinc 

H2S04 

K2Cr207 

Carbon 

2-1 

net,  Fuller,  etc.). 

Grove     . 

Zinc 

H2S04 

HNO3 

Platinum 

1-9 

Bunsen  . 

Zinc 

H2S04 

HN03 

Carbon 

1-9 

Leclanch4 
Lalande  . 

Zinc 
Zinc 

NH4C1 
KHO 

MnO2 
CuO 

Carbon 
Carbon 

1-4 

0-8 

Upward  . 

Zinc 

ZnCL 

Cl 

Carbon 

2-0 

Fitch      . 

Zinc 

NH4(J1 

KClO3+Na 

do. 

Carbon 

1-1 

Papst     . 
Obach  (dry)   . 

Iron 
Zinc 

NH4C1 

Fe2CI6 
Mn02 

Carbon 
Carbon 

0-4 

1-46 

in  CaSO4 

Class  III. 

Daniell(Meidinger 

Zinc 

ZnSO4 

CuSO4 

Copper 

1-07 

'  Minotto,  etc.) 

De  la  Hue 
Mari6Davy  . 

Zinc 

Zinc 

ZnCl2 

ZnSO, 

AgCl 
Hg2SO4 

Silver 
Carbon 

1-42 
1-4 

Clark  (Standard) 
Weston  . 

Zinc 
Cadmium 

ZnS04 
CdSO4 

Hg2SO4 

Mercury 
Mercury 

1-434 
1-025 

Von  Helmholtz      . 

Zinc 

ZnCl2 

Hg2Cl2 

Mercury 

i-o 

Class  IV. 

Accumulators. 

(Plant6,  Faure,  etc.) 

Lead 

H2S02 

Pb02 

Lead 

2-1  to  1-85 

19O.  Strength  of  Current.  —  The  student  must  not 
mistake  the  figures  given  in  the  above  table  for  the 
strength  of  current  which  the  various  batteries  will 
yield ;  the  current  depends,  as  was  said  in  Lesson  XIII., 
on  the  internal  resistance  of  the  cells  and  on  that  of  their 


CHAP.    ITI 


OHM'S  LAW  175 


circuit,  as  well  as  on  their  E.M.F.  The  E.M.F.  of  a  cell 
is  independent  of  its  size,  and  is  determined  solely  by  the 
materials  chosen  and  their  condition.  The  resistance 
depends  on  the  size  of  the  cell,  the  conducting  qualities 
of  the  liquid,  the  thickness  of  the  liquid  which  the  cur- 
rent must  traverse,  etc. 

The  definition  of  the  strength  of  a  current  is  as  fol- 
lows :  The  strength  of  a  current  is  the  quantity  of  electricity 
which  flows  past  any  point  of  the  circuit  in  one  second.* 
Suppose  that  at  the  end  of  10  seconds  25  coulombs  of 
electricity  to  have  passed  through  a  circuit,  then  the 
average  current  during  that  time  has  been  2|-  coulombs 
per  second,  or  2  \  amperes.  The  usual  strength  of  currents 
used  in  telegraphing  over  main  lines  is  only  from  five  to 
ten  thousandths  of  an  ampere. 

If  in  t  seconds  a  quantity  of  electricity  Q  has  flowed 
through  the  circuit,  then  the  current  C  during  that  time 
is  represented  by  the  equation 

c-f. 

This  should  be  compared  with  Art.  162. 

The  laws  which  determine  the  strength  or  quantity  of 
a  current  in  a  circuit  were  first  enunciated  by  Dr.  G.  S. 
Ohm,  who  stated  them  in  the  following  law :  — 

191.  Ohm's  Law. —  The  current  varies  directly  as  the 
electromotive-force,  and  inversely  as  the  resistance  of  the 
circuit;  or,  in  other  words,  anything  that  makes  the 

*  The  terms  "strength  of  current,"  "intensity  of  current,"  are  old- 
fashioned,  and  mean  no  more  than  "current"  means  —  that  is  to  say,  the 
number  of  amperes  that  are  flowing.  The  terms  "  strong,"  "great,"  and 
"  intense,"  as  applied  to  currents,  mean  precisely  the  same  thing.  Formerly, 
before  Ohm's  Law  was  properly  understood,  electricians  used  to  talk  about 
"quantity  currents"  and  "  intensity  currents,"  meaning  by  the  former 
term  a  current  flowing  through  a  circuit  in  which  there  is  very  small 
resistance  inside  the  battery  or  out ;  and  by  the  latter  expression  they 
designated  a  current  due  to  a  high  electromotive-force.  The  terms  were 
convenient,  but  should  be  avoided  as  misleading. 


176  ELECTRICITY   AND   MAGNETISM       PART  i 

E.M.F.  of  the  cell  greater  will  increase  the  current,  while 
anything  that  increases  the  resistance  (either  the  internal 
resistance  in  the  cells  themselves  or  the  resistance  of  the 
external  wires  of  the  circuit)  will  diminish  the  current. 
In  symbols  this  becomes 

E     r 
R  =  C' 

where  E  is  the  number  of  volts,  R  the  number  of  ohms 
of  the  circuit,  and  C  the  number  of  amperes  of  current. 

Example.  —  To  find  the  current  that  can  be  sent  through  a 
resistance  of  5  ohms  by  an  E.M.F.  of  20  volts.  20  -4-  5  =  4 
amperes. 

(See  further  concerning  Ohm's  Law  in  Lesson  XXXIII.) 
Ohm's  Law  says  nothing  about  the  energy  or  power  con- 
veyed by  a  current.  The  power  of  a  current  is  propor- 
tional both  to  the  current  and  to  the  electromotive-force 
which  drives  it  (see  Art.  435). 

192.  Resistance  and  Grouping  of  Cells.  — The  inter- 
nal resistances  of  the  cells  we  have  named  differ  very 
greatly,  and  differ  with  their  size.  Roughly  speaking, 
we  may  say  that  the  resistance  in  a  DanielPs  cell  is 
about  five  times  that  in  a  Grove's  cell  of  equal  size. 
The  Grove's  cell  has  indeed  both  a  higher  E.M.F.  and 
less  internal  resistance.  It  would  in  fact  send  a  current 
about  eight  times  as  strong  as  the  Daniell's  cell  of  equal 
size  through  a  short  stout  wire. 

We  may  then  increase  the  strength  of  a  battery  in 
two  ways :  — 

(1)  By  increasing  its  E.M.F. 

(2)  By  diminishing  its  internal  resistance. 

The  electromotive-force  of  a  cell  being  determined  by 
the  materials  of  which  it  is  made,  the  only  way  to  in- 
crease the  total  E.M.F.  of  a  battery  of  given  materials 
is  to  increase  the  number  of  cells  joined  "  in  series."  It 


CHAP,  in  KESISTANCE   OF  CELLS  177 

is  frequent  in  the  telegraph  service  to  link  thus  together 
two  or  three  hundred  of  the  flat  Darnell's  cells ;  and  they 
are  usually  made  up  in  trough-like  boxes,  containing  a 
series  of  10  cells,  as  shown  in  Fig.  106. 

To  diminish  the  internal  resistance  of  a  cell  the  follow- 
ing expedients  may  be  resorted  to  :  — 

(1)  The  plates  may  be  brought  nearer  together,  so 
that  the  current  shall   not  have  to  traverse  so  thick  a 
stratum  of  liquid. 

(2)  The  size  of  the  plates  may  be  increased,  as  this 


Fig.  106. 

affords  the  current,  as  it  were,  a  greater  number  of  pos- 
sible paths  through  the  stratum  of  liquid. 

(3)  The  zincs  of  several  cells  may  be  joined  together, 
to  form,  as  it  were,  one  large  zinc  plate,  the  coppers  being 
also  joined  to  form  one  large  copper  plate.  Suppose  four 
similar  cells  thus  joined  "  in  parallel,"  the  current  has  four 
times  the  available  number  of  paths  by  which  it  can 
traverse  the  liquid  from  zinc  to  copper;  hence  the  in- 
ternal resistance  of  the  whole  will  be  only  \  of  that  of 
a  single  cell.  But  the  E.M.F.  of  them  will  be  no  greater 
thus  than  that  of  one  cell.  • 

It  is  most  important  for  the  student  to  remember  that 
the  current  is  also  affected  by  the  resistances  of  the  wires 
of  the  external  circuit ;  and  if  the  external  resistance  be 


178  ELECTRICITY   AND   MAGNETISM        PART  i 

already  great,  as  in  telegraphing  through  a  long  line,  it 
is  little  use  to  diminish  the  internal  resistance  if  this  is 
already  much  smaller  than  the  resistance  of  the  line  wire. 
It  is,  on  the  contrary,  advantageous  to  increase  the  num- 
ber of  cells  in  series,  though  every  cell  adds  a  little  to  the 
total  resistance. 

Example.  —  If  the  line  has  a  resistance  of  1000  ohms,  and  five 
cells  are  used  each  of  which  has  an  E.M.F.  of  1*1  volt 
and  an  internal  resistance  of  3  ohms.  By  Ohm's  Law 
the  current  will  be  5'5  •*- 1015 ;  or  0-0054  ampere.  If 
now  eight  cells  are  used,  though  the  total  resistance  is 
thereby  increased  from  1015  to  1040  ohms,  yet  the 
E.M.F.  is  increased  from  5'5  to  8'8  volts,  and  the 
current  to  0*0085  ampere. 

The  E.M.F.  of  the  single-fluid  cells  of  Volta  and  Smee 
is  marked  in  the  table  as  doubtful,  for  the  opposing 
E.M.F.  of  polarization  sets  in  almost  before  the  true 
E.M.F.  of  the  cell  can  be  measured.  The  different  values 
assigned  to  other  cells  are  accounted  for  by  the  different 
degrees  of  concentration  of  the  liquids.  Thus  in  the 
Daniell's  cells  used  in  telegraphy,  water  only  is  supplied 
at  first  in  the  cells  containing  the  zincs ;  and  the  E.M.F. 
of  these  is  less  than  if  acid  or  sulphate  of  zinc  were  added 
to  the  water. 

193.  Other  Batteries.  —  Numerous  other  forms  of 
battery  have  been  suggested  by  different  electricians. 
There  are  three,  of  theoretical  interest  only,  in  which, 
instead  of  using  two  metals  in  one  liquid  which  attacks 
them  unequally,  two  liquids  are  used  having  unequal 
chemical  action  on  the  metal.  In  these  there  is  no  con- 
tact of  dissimilar  metals.  The  first  of  these  was  invented 
by  the  Emperor  Napoleon  III.  Both  plates  were  of  cop- 
per dipping  respectively  into  solutions  of  dilute  sulphuric 
acid  and  of  .cyanide  of  potassium,  separated  by  a  porous 
cell.  The  second  of  these  combinations,  due  to  Wb'hler, 
employs  plates  of  aluminium  only,  dipping  respectively 
into  strong  nitric  acid  and  a  solution  of  caustic  soda.  In 


CHAP,  in  MISCELLANEOUS   CELLS  179 

the  third,  invented  by  Dr.  Fleming,  the  two  liquids  do 
not  even  touch  one  another,  being  joined  together  by  a 
second  metal.  In  this  case  the  liquids  chosen  are  sodium 
persulphide  and  nitric  acid,  and  the  two  metals  copper 
and  lead.  A  similar  battery  might  be  made  with  copper 
and  zinc,  using  solutions  of  ordinary  sodium  sulphide,  and 
dilute  sulphuric  acid  in  alternate  cells,  a  bent  zinc  plate 
dipping  into  the  first  and  second  cells,  a  bent  copper  plate 
clipping  into  second  and  third,  and  so  on  ;  for  the  electro- 
motive-force of  a  copper-sodium-sulphide-zinc  combination 
is  in  the  reverse  direction  to  that  of  a  copper-sulphuric 
acid-zinc  combination. 

Upward  proposed  a  chlorine  battery,  having  slabs  of 
zinc  immersed  in  chloride  of  zinc  and  kathodes  of  carbon 
surrounded  by  crushed  carbon  in  a  porous  pot,  gaseous 
chlorine  being  pumped  into  the  cells,  and  dissolving  into 
the  liquids  to  act  as  a  depolarizer.  It  has  an  E.M.F.  of 
2  volts. 

Bennett  described  a  cheap  and  most  efficient  battery, 
in  which  old  meat-canisters  packed  with  iron  filings 
answer  for  the  positive  element,  and  serve  to  contain 
the  exciting  liquid,  a  strong  solution  of  caustic  soda. 
Scrap  zinc  thrown  into  mercury  in  a  shallow  inner  cup 
of  porcelain  forms  the  anode. 

Marie  Davy  employed  a  cell  in  which  the  zinc  dipped 
into  sulphate  of  zinc,  while  a  carbon  plate  dipped  into  a 
pasty  solution  of  mercurous  sulphate.  When  the  cell  is 
in  action  mercury  is  deposited  on  the  surface  of  the  car- 
bon, so  that  the  cell  is  virtually  a  zinc-mercury  cell.  It 
was  largely  used  for  telegraphy  in  France  before  the 
introduction  of  the  Leclanche  cell. 

Obach's  dry  cell  has  an  outer  cylinder  of  zinc  which 
serves  as  a  case,  lined  with  plaster  of  Paris  soaked  in 
salammoniac ;  with  a  central  carbon  kathode  surrounded 
with  binoxide  of  manganese  mixed  with  graphite. 

The  Fitch  cell,  used  in  the  United  States,  is  a  zinc- 
carbon  cell  with  an  excitant  composed  of  salammoniac 


180  ELECTRICITY  AND   MAGNETISM       PART  i 

solution  to  which  the  chlorates  of  potash  and  soda  have 
been  added. 

Papst  used  an  iron-carbon  cell  with  ferric  chloride 
solution  as  excitant.  The  iron  dissolves  and  chlorine  is 
at  first  evolved,  but  without  polarization ;  the  liquid 
regenerating  itself  by  absorbing  moisture  from  the  air. 
It  is  very  constant  but  of  low  E.M.F. 

Jablochkoif  described  a  battery  in  which  plates  of 
carbon  and  iron  are  placed  in  fused  nitre ;  the  carbon  is 
here  the  electropositive  element,  being  rapidly  consumed 
in  the  liquid. 

Plante's  and  Faure's  Secondary  Batteries,  and  Grove's 
Gas  Battery,  are  described  in  Arts.  492,  493. 

The  so-called  Dry  Pile  of  Zamboni  deserves  notice. 
It  consists  of  a  number  of  paper  disks,  coated  with  zinc- 
foil  on  one  side  and  with  binoxide  of  manganese  on  the 
other,  piled  upon  one  another,  to  the  number  of  some 
thousands,  in  a  glass  tube.  Its  internal  resistance  is 
enormous,  as  the  internal  conductor  is  the  moisture  of 
the  paper,  and  this  is  slight ;  but  its  electromotive-force 
is  very  great,  and  a  good  dry  pile  will  yield  sparks. 
Many  years  may  elapse  before  the  zinc  is  completely 
oxidized  or  the  manganese  exhausted.  In  the  Clarendon 
Laboratory  at  Oxford  there  is  a  dry  pile,  the  poles  of 
which  are  two  metal  bells  :  between  them  is  hung  a  small 
brass  ball,  which,  by  oscillating  to  and  fro,  slowly  dis- 
charges the  electrification.  It  has  now  been  continuously 
ringing  the  bells  for  fifty  years. 

194.  Effect  of  Heat  on  Cells.  —  If  a  cell  be  warmed 
it  yields  a  stronger  current  than  when  cold.  This  is 
chiefly  due  to  the  fact  that  the  liquids  conduct  better 
when  warm,  the  internal  resistance  being  thereby  reduced. 
A  slight  change  is  also  observed  in  the  E.M.F.  on  heat- 
ing ;  thus  the  E.M.F.  of  a  Daniell's  cell  is  about  1£  per 
cent  higher  when  warmed  to  the  temperature  of  boiling 
water,  while  that  of  a  bichromate  battery  falls  off 
nearly  2  per  cent  under  similar  circumstances.  In  the 


CHAP,  in     MAGNETIC   EFFECTS   OF   CURKENT      181 

Clark  standard  cell  the  E.M.F.  decreases  slightly  with 
temperature,  the  coefficient  being  0-00077  per  degrees 
centigrade.  Its  E.M.F.  at  any  temperature  0  may  be 
calculated  by  the  formula, 

E.M.F.  =  1434  [1  -  0-00077  (0  -  15)  ]  volt. 


LESSON  XVI.  —  Magnetic  Actions  of  the  Current 

195.  Oersted's   Discovery.  —  A   connexion    of    some 
kind  between  magnetism  and  electricity  had  long  been 
suspected.      Lightning  had  been   known   to   magnetize 
knives  and  other  objects  of  steel ;  but  almost  all  attempts 
to  imitate  these  effects  by  powerful  charges  of  electricity, 
or  by  sending  currents  of  electricity  through  steel  bars, 
had  failed.*     About  1802  Romagnosi,  of  Trente,  vaguely 
observed  that   a  voltaic   pile   affects   a  compass-needle. 
The  true  connexion  between  magnetism  and  electricity 
remained,  however,  to  be  discovered. 

In  1819,  Oersted,  of  Copenhagen,  showed  that  a  mag- 
net tends  to  set  itself  at  right  angles  to  a  wire  carrying  an 
electric  current.  He  also  found  that  the  way  in  which 
the  needle  turns,  whether  to  the  right  or  the  left  of  its 
usual  position,  depends  upon  the  position  of  the  wire  that 
carries  the  current  — whether  it  is  above  or  below  the 
needle,  —  and  on  the  direction  in  which  the  current  flows 
through  the  wire. 

196.  Oersted's    Experiment.  —  Very  simple   appara- 
tus suffices  to  repeat  the  fundamental  experiment.     Let 
a  magnetic  needle  be  suspended  on  a  pointed  pivot,  as 
in  Fig.  107.     Above  it,  and  parallel  to  it,  is  held  a  stout 

*  Down  to  this  point  in  these  lessons  there  has  been  no  connexion 
between  magnetism  and  electricity,  though  something  has  been  said  about 
each.  The  student  who  cannot  remember  whether  a  charge  of  electricity 
does  or  does  not  affect  a  magnet,  should  turn  back  to  what  was  said  in 
Art.  99. 


182 


ELECTRICITY   AND   MAGNETISM       PART  i 


copper  wire,  one  end  of  which  is  joined  to  one  pole  of  a 
battery  of  one  or  two  cells.  The  other  end  of  the  wire 
is  then  brought  into  contact  with  the  other  pole  of  the 
battery.  As  soon  as  the  circuit  is  completed  the  current 
flows  through  the  wire  and  the  needle  turns  briskly  aside. 
If  the  current  be  flowing  along  the  wire  above  the  needle 
in  the  direction  from  north  to  south,  it  will  cause  the 
N-seeking  end  of  the  needle  to  turn  eastwards ;  if  the 
current  flows  from  south  to  north  in  the  wire  the  N-seek- 


Fig.  107. 

ing  end  of  the  needle  will  be  deflected  westwards.  If  the 
wire  is,  however,  beloiv  the  needle,  the  motions  will  be 
reversed,  and  a  current  flowing  from  north  to  south  will 
cause  the  N-seeking  pole  to  turn  westwards. 

197.  Ampere's  Rule.  —  To  keep  these  movements  in 
memory,  Ampere  suggested  the  following  fanciful  but 
useful  rule.  Suppose  a  man  swimming  in  the  wire  with 
the  current,  and  that  he  turns  so  as  to  face  the  needle,  then 
the  N-seeking  pole  of  the  needle  will  be  deflected  towards  his 
left  hand.  In  other  words,  the  deflexion  of  the  N-seeking 
pole  of  a  magnetic  needle,  as  viewed  from  the  conductor, 
is  towards  the  left  of  the  current. 

For  certain  particular  cases  in  which  a  fixed  magnet 
pole  acts  on  a  movable  circuit,  the  following  converse  to 


CHAP.    Ill 


GALVANOSCOPE 


183 


Fig.  108. 


Ampere's  Rule  will  be  found  convenient.  Suppose  a  man 
swimming  in  the  wire  with  the  current,  and  that  he  turns 
so  as  to  look  along  the  direction  of  the  lines  of  force  of 
the  pole  (i.e.  as  the  lines  of  force  run,  from  the  pole  if  it 
be  N-seeking,  towards  the  pole  if  it  be  S-seeking),  then  he 
and  the  conducting  wire  with  him  will  be  urged  toward 
his  left. 

198.  Corkscrew  Rule.  —  More  convenient  is  the  fol- 
lowing rule  suggested  by  Maxwell.     The  direction  of  the 
current  and  that  of  the  resulting  magnetic  force  are  related 
to   one    another,    as   are    the    rotation   and 

the  forward  travel  of  an  ordinary  (right- 
handed)  corkscrew.  In  Fig.  108,  if  the 
circle  represents  the  circulation  of  current, 
the  arrow  gives  the  direction  of  the  result- 
ing magnetic  force.  One  advantage  of 
this  rule  is,  that  it  is  equally  applicable 
in  the  other  case.  If  the  arrow  represents  the  direction 
of  the  current  along  a  straight  wire,  the  circle  will 
represent  the  direction  of  the  resulting  magnetic  force 
around  it. 

199.  Galvanoscope.  —  A    little     consideration    will 
show  that  if  a  current  be  carried  below  a  needle  in  one 

direction,  and  then  back  in  the  opposite 
direction  above  the  needle,  by  bending 
the  wire  round,  as  in  Fig.  109,  the 
forces  exerted  on  the  needle  by  both 
portions  of  the  current  will  be  in  the 
same  direction.  For  let  a  be  the 
N-seeking,  and  b  the  S-seeking,  pole 
of  the  suspended  needle,  then  the 
tendency  of  the  current  in  the  lower 
part  of  the  wire  will  be  to  turn  the 
needle  so  that  a  comes  towards  the  observer,  while  I) 
retreats;  while  the  current  flowing  above,  which  also 
deflects  the  N-seeking  pole  to  its  left,  will  equally  urge 
a  towards  the  observer,  and  b  from  him.  The  needle 


.  109. 


184  ELECTRICITY  AND  MAGNETISM       PART  i 

will  not  stand  out  completely  at  right  angles  to  the 
direction  of  the  wire  conductor,  but  will  take  an  oblique 
position.  The  directive  forces  of  the  earth's  magnetism 
are  tending  to  make  the  needle  point  north-and-south. 
The  electric  current  is  acting  on  the  needle,  tending 
to  make  it  set  itself  west-and-east.  The  resultant 
force  will  be  in  an  oblique  direction  between  these, 
and  will  depend  upon  the  relative  strength  of  the  two 
conflicting  forces.  If  the  current  is  very  strong  the 
needle  will  turn  widely  round  ;  but  could  only  turn  com- 
pletely to  a  right  angle  if  the  current  were  infinitely 
strong.  If,  however,  the  current  is  feeble  in  comparison 
with  the  directive  magnetic  force,  the  needle  will  turn 
very  little. 

This  arrangement  will,  therefore,  serve  roughly  as  a 
Galvanoscope  or  indicator  of  currents ;  for  the  move- 
ment of  the  needle  shows  the  direction  of  the  current, 
and  indicates  whether  it  is  a  strong  or  a  weak  one. 
This  apparatus  is  too  rough  to  detect  very  delicate  cur- 
rents. To  obtain  a  more  sensitive  instrument  there  are 
two  possible  courses:  (i.)  increase  the  effective  action 
of  the  current  by  carrying  the  wire  more  than  once 
round  the  needle;  (ii.)  decrease  the  opposing  directive 
force  of  the  earth's  magnetism  by  some  compensating 
contrivance. 

2OO.  Schweigger's  Multiplier.  —  The  first  of  the 
above  suggestions  was  carried  out  by  Schweigger,  wlio 
constructed  a  multiplier  of  many  turns  of  wire.  A  suit- 
able frame  of  wood,  brass,  or  ebonite,  is  prepared  to 
receive  the  wire,  which  must  be  "  insulated,"  or  covered 
with  silk,  or  cotton,  or  guttapercha,  to  prevent  the 
separate  turns  of  the  coil  from  coming  into  contact  with 
each  other.  Within  this  frame,  which  may  be  circular, 
elliptical,  or  more  usually  rectangular,  as  in  Fig.  110,  the 
needle  is  suspended,  the  frame  being  placed  so  that 
the  wires  lie  in  the  magnetic  meridian.  The  greater  the 
number  of  turns  the  more  powerful  will  be  the  magnetic 


CHAP.    Ill 


ASTATIC   COMBINATIONS 


185 


deflexion  produced  by  the  passage  of  equal  quantities  of 
current.  But  if  the  wire  is  thin,  or  the  number  of  turns 
of  wire  numerous,  the 
resistance  thereby  offered 
to  the  flow  of  electricity 
may  very  greatly  reduce 
the  strength  of  the  current. 
The  student  will  grasp  the 
importance  of  this  observa- 
tion when  he  has  read  the 
chapter  on  Ohm's  Law. 
Gumming,  of  Cambridge, 
appears  to  have  been  the 
first  to  use  a  coil  surround- 
ing a  pivoted  needle  to 
measure  the  current.  To 


Fig.  110. 
him  we  owe  the  term  Gal- 


vanometer. 

2O1.  Astatic  Combinations.  —  The  directive  force  ex- 
ercised by  the  earth's  magnetism  on  a  magnetic  needle 
may  be  reduced  or  obviated  by  one  of  two  methods  :  — 

(a)  \_Haiiy's  Method"].  By  employing  a  compensating 
magnet.  An  ordinary  long  bar  magnet  laid  in  the  mag- 
netic meridian,  but  with  its  N-seeking  pole  directed 
towards  the  north,  will,  if  placed  horizontally  above  or 
below  a  suspended  magnetic  needle,  tend  to  make  the 
needle  set  itself  with  its  S-seeking  pole  northwards.  If 
ne&r  the  needle  it  may  overpower  the  directive  force  of 
the  earth,  and  cause  the  needle  to  reverse  its  usual  posi- 
tion. If  it  is  far  away,  all  it  can  do  is  to  lessen  the 
directive  force  of  the  earth.  At  a  certain  distance  the 
magnet  will  just  compensate  this  force,  and  the  needle 
will  be  neutral.  This  arrangement  for  reducing  the 
earth's  directive  force  is  applied  in  the  reflecting  galva- 
nometer shown  in  Fig.  122,  in  which  the  magnet  at  the 
top,  curved  in  form  and  capable  of  adjustment  to  any 
height,  affords  a  means  of  adj  usting  the  instrument  to  the 
desired  degree  of  sensitiveness  by  raising  or  lowering  it. 


186 


ELECTRICITY  AND   MAGNETISM       PART  i 


(&)  [Nobili's  Method}.  By  using  an  astatic  pair  of 
magnetic  needles.  If  two  magnetized  needles  of  equal 
strength  and  size  are  bound  together  by  a  light  wire  of 
brass,  or  aluminium,  in  re- 
versed positions,  as  shown 
in  Fig.  Ill,  the  force  urging 
one  to  set  itself  in  the  mag- 
netic meridian  is  exactly 
counterbalanced  by  the  force 
that  acts  on  the  other.  Con- 
sequently this  pair  of  needles 
will  remain  in  any  position 
in  which  it  is  set,  and  is 
independent  of  the  earth's 
magnetism.  Such  a  com- 
bination is  known  as  an  astatic  pair.  It  is,  however, 
difficult  in  practice  to  obtain  a  perfectly  astatic  pair, 
since  it  is  not  easy  to  magnetize  two  needles  exactly 
to  equal  strength,  nor  is  it  easy  to  fix 
them  perfectly  parallel  to  one  another. 
Such  an  astatic  pair  is,  however,  readily 
deflected  by  a  current  flowing  in  a  wire 
coiled  around  one  of  the  needles ;  for, 
as  shown  in  Fig.  112,  the  current 
which  flows  above  one  needle  and 
below  the  other  will  urge  both  in  the 
same  direction,because  they  are  already 
in  reversed  positions.  It  is  even  pos- 
sible to  go  further,  and  to  carry  the 


Fig.  111. 


Fig.  112. 


wire  round  both  needles,  winding  the  coil  around  the 
upper  in  the  opposite  sense  to  that  in  which  the  coil  is 
wound  round  the  lower  needle.  Several  other  astatic 
combinations  are  possible.  For  example,  two  needles 
may  be  set  vertically,  with  similar  poles  upward,  at  the 
ends  of  a  pivoted  horizontal  strip  of  wood  or  brass. 

Nobili  applied  the  astatic  arrangement  of  needles  to 
the  multiplying  coils  of  Schweigger,  and  thus  constructed 


CHAP,  in  MAGNETIC    WHIRLS  187 

a  very  sensitive  instrument,  the  Astatic  Galvanometer, 
shown  in  Fig.  119.  The  special  forms  of  galvanometer 
adapted  for  the  measurement  of  currents  are  described 
in  the  next  lesson. 

2O2.  Magnetic  Field  due  to  Current:  Magnetic 
Whirls.  —  Arago  found  that  if  a  current  be  passed 
through  a  piece  of  copper  wire  it  becomes  capable  of 
attracting  iron  filings  to  it  so  long  as  the  current  flows. 
These  filings  set  themselves  at  right  angles  to  the  wire* 
and  cling  around  it,  but  drop  off  when  the  circuit  is 
broken.  There  is,  then,  a  magnetic  "  field,"  around  the 
wire  which  carries  the 
current;  and  it  is  im-  ^  ^ 


portant  to  know  how  the      '          N*  /  ^ 

lines    of    force    are    dis-   \.  4t     /  ^     05 £ 

tributed  in  this  field.  *^ /  \i  '/* 

Let  the  central  spot  in  ^ 

Fig.  113  represent  an  im- 
aginary cross-section  of  the  wire,  and  let  us  suppose  the 
current  to  be  flowing  in  through  the  paper  at  that  point. 
Then  by  Ampere's  rule  a  magnet  needle  placed  below  will 
tend  to  set  itself  in  the  position  shown,  with  its  N  pole 
pointing  to  the  left.*  The  current  will  urge  a  needle 
above  the  wire  into  the  reverse  position.  A  needle  on 
the  right  of  the  current  will  set  itself  at  right  angles  to 
the  current  (i.e.  in  the  plane  of  the  paper),  and  with  its 
N"  pole  pointing  dotvn,  while  the  N"  pole  of  a  needle  on 
the  left  would  be  urged  up.  In  fact  the  tendency  would 
be  to  urge  the  N  pole  round  the  conductor  in  the  same 


*  If  the  student  has  any  difficulty  in  applying  Ampfere's  rule  to  this 
case  and  the  others  which  succeed ,  he  should  carefully  follow  out  the  fol- 
lowing mental  operation.  Consider  the  spot  marked  "  in "  as  a  hole  in 
the  ground  into  which  the  current  is  flowing,  and  into  which  he  dives 
head-foremost.  While  in  the  hole  he  must  turn  round  so  as  to  face  each 
of  the  magnets  in  succession,  and  remember  that  in  each  case  the  N- 
seeking  pole  will  be  urged  to  his  left.  In  diagram  84  he  must  conceive 
himself  as  coming  up  out  of  the  hole  in  the  grourd  where  the  current  is 
flowing  out. 


188  ELECTRICITY  AND  MAGNETISM       PART  i 

way  as  the  hands  of  a  watch  move ;  while  the  S  pole 
would  be  urged  in  the  opposite  cyclic  direction  to  that  of 
the  hands  of  a  watch.  If  the  current  is  reversed,  and  is 
regarded  as  flowing  towards  the  reader,  i.e.  coming  up 
out  of  the  plane  of  the  paper,  as  in  the  diagram  of  Fig. 
114,  then  the  motions  would  be  just  in  the  reverse  sense. 
It  would  seem  from  this  as  if  a  N-seeking  pole  of  a 
magnet  ought  to  revolve  continuously  round  and  round  a 
current ;  but  as  we  cannot  obtain  a  magnet  with  one 
pole  only,  and  as  the  S-seeking  pole  is  urged  in  an  oppo- 
site direction,  all  that  occurs  is  that  the  needle  sets  itself 
as  a  tangent  to  a  circular  curve 
surrounding  the  conductor.  The 
field  surrounding  the  conductor 
consists  in  fact  of  a  sort  of  en- 
veloping magnetic  whirl  all  along 
it,  the  whirl  being  strong  near 
the  wire  and  weaker  farther  away. 
This  is  what  Oersted  meant  when 
he  described  the  electric  current 
F.  'j15  as  acting  "  in  a  revolving  manner  " 

upon  the  magnetic  needle.  The 
field  of  force,  with  its  circular  lines  surrounding  a  current 
flowing  in  a  straight  conductor,  can  be  examined  experi- 
mentally with  iron  filings  in  the  following  way :  A  card 
is  placed  horizontally  and  a  stout  copper  wire  is  passed 
vertically  through  a  hole  in  it  (Fig.  115).  Iron  filings 
are  sifted  over  the  card  (as  described  in  Art.  119),  and  a 
strong  current  from  three  or  four  large  cells  is  passed 
through  the  wire.  On  tapping  the  card  gently  the  filings 
near  the  wire  set  themselves  in  concentric  circles  round  it. 
It  is  because  of  this  surrounding  field  that  two  con- 
ductors can  apparently  act  on  one  another  at  a  distance. 
If  both  currents  are  flowing  in  the  same  direction,  their 
magnetic  fields  tend  to  merge,  and  the  resulting  stress  in 
the  medium  tends  to  drag  them  together  with  an  appa- 
rent attraction.  If  the  currents  are  flowing  in  opposite 


CHAP.    Ill 


MAGNETIC   SHELL 


directions  the  stresses  in  the  intervening  magnetic  field 
tend  to  thrust  them  apart  (see  also  Art.  389). 

It  is  known  that  energy  has  to  be  spent  in  producing 
any  magnetic  field.  When  a  current  is  turned  on  in  a 
wire  the  magnetic  field  grows  around  the  wire,  some  of 
the  energy  of  the  battery  being  used  during  the  growth 
of  the  current  for  that  purpose.  One  reason  why  electric 
currents  do  not  instantly  rise  to  their  final  value  is  be- 
cause of  the  reactive  effect  of  this  surrounding  magnetic 
field.  No  current  can  exist  without  this  surrounding- 
magnetic  field.  Indeed  it  is  impossible  to  refute  the 
proposition  that  what  we  commonly  call  an  electric 
current  in  a  wire  really  is  this  external  magnetic 
whirl. 

203.  Equivalent  Magnetic  Shell :  Ampere's  Theorem. 
—  For  many  purposes  the  following  way  of  regarding 
the  magnetic  action  of  electric  currents  is  more  con- 
venient than  the  preceding.  Suppose  we  take  a  battery 
and  connect  its  terminals  by  a  circuit  of  wire,  and  that 


Fig.  116. 

a  portion  of  the  circuit  be  twisted,  as  in  Fig.  116,  into 
a  looped  curve,  it  will  be  found  that  the  entire  space 
enclosed  by  the  loop  possesses  magnetic  properties.  In 
our  figure  the  current  is  supposed  to  be  flowing  round 


190  ELECTRICITY   AND  MAGNETISM        PART  i 

the  loop,  as  viewed  from  above,  in  the  same  direction  as 
the  hands  of  a  clock  move  round ;  an  imaginary  man 
swimming  round  the  circuit  and  always  facing  towards 
the  centre  would  have  his  left  side  down.  By  Ampere's 
rule,  then,  a  N  pole  would  be  urged  downwards  through 
the  loop,  while  a  S  pole  would  be  urged  upwards.  In 
fact  the  space  enclosed  by  the  loop  of  the  circuit  behaves 
like  a  magnetic  shell  (see  Art.  118),  having  its  upper  face 
of  S-seeking  magnetism,  and  its  lower  face  of  N-seeking 
magnetism.  It  can  be  shown  in  every  case  that  a  closed 
voltaic  circuit  is  equivalent  to  a  magnetic  shell  whose  edges 
coincide  in  position  with  the  circuit,  the  shell  being  of 
such  a  strength  that  the  number  of  its  lines  of  force 
is  the  same  as  that  of  the  lines  of  force  due  to  the 
current  in  the  circuit.  The  circuit  acts  on  a  magnet 
attracting  or  repelling  it,  and  being  attracted  or  repelled 
by  it,  just  exactly  as  its  equivalent  magnetic  shell  would 
do.  Also,  the  circuit  itself,  when  placed  in  a  magnetic 
field,  experiences  the  same  force  as  its  equivalent  mag- 
netic shell  would  do. 

204.  Maxwell's   Rule.  —  Professor   Clerk   Maxwell, 
who  developed  this  method  of  treating  the  subject,  has 
given  the   following  elegant   rule  for   determining   the 
mutual  action  of  a  circuit  and  a  magnet  placed  near  it. 
Every  portion  of  the  circuit  is  acted  upon  by  a  force  urging 
it  in  such  a  direction  as  to  make  it  enclose  within  its  embrace 
the  greatest  possible  number  of  lines  of  force.     If  the  cir- 
cuit is  fixed  and  the  magnet  movable,  then  the  force 
acting  on  the  magnet  will  also  be  such  as  to  tend  to 
make  the  number  of  lines  of  force  that  pass  through 
the  circuit  a  maximum  (see  also  Art.  349). 

This  is  but  one  case  of  the  still  more  general  law 
governing  every  part  of  every  electromagnetic  system, 
viz. :  Every  electromagnetic  system  tends  so  to  change  the 
configuration  of  its  parts  as  to  make  the  flux  of  magnetic 
lines  through  the  exciting  circuit  a  maximum.  (Art.  379.) 

205.  De  la  Rive's  Floating  Battery. —  The  preced- 


CHAP.    Ill 


FLOATING  BATTERY 


191 


ing  remarks  may  be  illustrated  experimentally  by  the 
aid  of  a  little  floating  battery.  A  plate  of  zinc  and  one 
of  copper  (see  Fig.  117)  are  fixed  side  by  side  in  a  large 
cock,  and  connected  above  by  a  coil  of  several  windings  of 
covered  copper  wire.  This  is  floated  upon  a  dish  contain- 
ing dilute  sulphuric  acid.  If  one  pole  of  a  bar  magnet 
be  held  towards  the  ring  it  will  be  attracted  or  repelled 
according  to  the  pole  employed.  The  floating  circuit  will 
so  move  as  to  make  the  flux  of  magnetic  lines  through  the 


Fig.  117. 

coil  a  maximum.  If  the  S  pole  of  the  magnet  be  pre- 
sented to  that  face  of  the  ring  which  acts  as  a  S-seekiug 
pole  (viz.  that  face  round  which  the  current  is  flowing  in 
a  clockwise  direction),  it  will  repel  it.  If  the  pole  be 
thrust  right  into  the  ring,  and  then  held  still,  the  battery 
will  be  strongly  repelled,  will  draw  itself  off,  float  away, 
turn  round  so  as  to  present  toward  the  S  pole  of  the 
magnet  its  N-seeking  face,  will  then  be  attracted  up,  and 
will  thread  itself  on  to  the  magnet  up  to  the  middle,  in 


192  ELECTRICITY  AND   MAGNETISM        PART  i 

which  position  as  many  magnetic  lines  of  force  as  pos- 
sible cross  the  area  of  the  ring. 

It  can  be  shown  also  that  two  circuits  traversed  by 
currents  attract  and  repel  one  another  just  as  two  mag- 
netic shells  would  do. 

It  will  be  explained  in  Lesson  XXXI.  on  Electromag- 
nets how  a  piece  of  iron  or  steel  can  be  magnetized  by 
causing  a  current  to  flow  in  a  spiral  wire  round  it. 

206.  Strength  of  the  Current  in  Magnetic  Measure. 
—  When  a  current   thus  acts   on    a   magnet  pole   near 

it,  the  force  /  which  it  exerts  will  be  proportional  to 
the  strength  C  of  the  current,  and  proportional  also  to 
the  strength  m  of  the  magnet  pole,  and  to  the  length  / 
of  the  wire  employed :  the  force  exerted  between  each  ele- 
ment of  the  circuit  and  the  pole  will  also  vary  inversely  as 
the  square  of  the  distance  r  between  them.  If  the  wire 
is  looped  into  a  circular  coil  with  the  magnet  pole  at  the 
centre,  so  that  each  portion  of  the  circuit  is  approximately 

at  the  same    distance    from    the   pole,  /  =  — y  dynes. 

Suppose  the  wire  looped  up  into  a  circle  round  the  magnet 

2   C1 

pole,  then  I  =  Zirr,  and  f  =  -   -  m  dynes.     Suppose  also 

that  the  circle  is  of  one  centimetre  radius,  and  that  the 
magnet  pole  is  of  strength  of  one  unit  (see  Art.  352), 
then  the  force  exerted  by  the  current  of  strength  C 

2  C 
will  be x  1,  or  2?rC  dynes.     In  order,  therefore,  that 

a  current  of  strength  C  should  exert  a  force  of  C  dynes  on 
the  unit  pole,  one  must  consider  the  current  as  travelling 

round  only  7  -  part  of  the  circle,  or  round  a  portion  of 

&7T 

the  circumference  equal  in  length  to  the  radius. 

207.  Unit  of  Current.  —  A  current  is  said  to  have  a 
strength  of  one  "  absolute  "  unit  when  it  is  such  that  if  one 
centimetre  length  of  the  circuit  is  bent  into  an  arc  of  one 
centimetre  radius,  the  current  in  it  exerts  a  force  of 


CHAP,  in  GALVANOMETERS  193 

one  dyne  on  a  magnet-pole  of  unit  strength  placed  at  the 
centre  of  the  arc.  The  practical  unit  of  "  one  ampere  "  is 
only  -jig-  of  this  theoretical  unit  (see  also 
Art.  354). 

If  the  wire,  instead  of  being  looped  into  a 
coil,  is  straight  and  of  indefinite  length,  the 
force  which  the  current  in  it  exerts  upon  a 
pole  of  strength  m  placed   at  point   P  near 
it  will    be  found   to   vary   inversely   as   the 
simple  distance  (not  as  the  square),  and  the 
pole  will  tend  to  move  at  right  angles  both 
to  the  wire  and  to  the  line  OP.     In  Fig.  118 
the    descending    current   will   (according  to        lg' 
the  corkscrew  rule  above)  tend  to  drive  a  N  pole  at  P 
towards  the  spectator.      If  the  current  is  C  amperes  the 
force  (in  dynes)  on  the  pole  of  m  units  will  (see  Art.  343)  be 

/=2mC/10r. 

Example.  —  The  force  exerted  by  a  current  of  00  amperes 
in  a  long  straight  conductor  upon  a  pole  of  200  units 
placed  2  centimetres  away  from  it  will  be  1200  dynes, 
or  (dividing  by  g  =  981)  about  1*22  grammes'  weight. 


LESSON  XVII.  —  Galvanometers 

208-  The  term  Galvanometer  is  applied  to  an  in- 
strument for  measuring  the  strength  of  electric  currents 
by  means  of  their  electromagnetic  action.  There  are 
two  general  classes  of  Galvanometers  :  (1)  those  in  which 
the  current  flowing  in  a  fixed  coil  of  wire  causes  the 
deflexion  of  a  pivoted  or  suspended  magnetic  needle ;  (2) 
those  in  which  the  current  flowing  in  a  movable  coil 
suspended  between  the  poles  of  a  fixed  magnet  causes  the 
coil  to  turn.  There  is  a  third  kind  of  instrument  (called 
for  distinction  electrodynamometer,  see  Art.  394),  in  which 
both  the  moving  part  and  the  fixed  part  are  coils.  These 
last  are  used  chiefly  for  alternating-currents. 


194  ELECTRICITY  AND  MAGNETISM       PART  i 

The  simple  arrangement  described  in  Art.  199  was 
termed  a  "  Galvanoscope,"  or  current  indicator,  but  it 
could  not  rightly  be  termed  a  "  galvanometer  "  *  or  current 
measurer,  because  its  indications  were  only  qualitative,  not 
quantitative.  The  indications  of  the  needle  did  not  afford 
accurate  knowledge  as  to  the  exact  strength  of  current 
flowing  through  the  instrument.  A  good  galvanometer 
must  fulfil  the  essential  condition  that  its  readings  shall 
really  measure  the  strength  of  the  current  in  some  cer- 
tain way.  It  should  also  be  sufficiently  sensitive  for  the 
currents  that  are  to  be  measured  to  affect  it.  The 
galvanometer  adapted  for  measuring  very  small  currents 
(say  a  current  of  only  one  or  two  millionth  parts  of  an 
ampere)  will  not  be  suitable  for  measuring  very  strong 
currents,  such  as  are  used  in  electric  lighting  or  electro- 
plating. Large  currents  need  thick  wires ;  and  a  coil  of  few 
turns  will  suffice.  If  very  small  currents  are  to  turn  the 
needle  they  must  circulate  hundreds  or  thousands  of  times 
around  it,  and  therefore  a  coil  of  many  turns  is  appro- 
priate, and  the  wire  may  be  a  very  fine  one.  Moreover, 
if  the  current  to  be  measured  has  already  passed  through 
a  circuit  of  great  resistance  (as,  for  example,  some  miles 
of  telegraph  wire),  a  galvanometer  whose  coil  is  a  short 
one,  consisting  only  of  a  few  turns  of  wire,  will  be  of  no 
use,  and  a  long-coil  galvanometer  must  be  employed  with 
many  hundreds  or  even  thousands  of  turns  of  insulated 
wire  round  the  needle.  The  reason  of  this  is  explained 
hereafter  (Art.  408).  Hence  it  will  be  seen  that  different 
styles  of  instrument  are  needed  for  different  kinds  of 
works ;  but  of  all  it  is  required  that  they  should  afford 
quantitative  measurements,  that  they  should  be  sufficiently 
sensitive  for  the  current  that  is  to  be  measured,  and  carry 
that  current  without  overheating. 

*  The  terms  Rheoscope  and  Rheometer  are  still  occasionally  applied  to 
these  instruments.  A  current  interrupter  is  sometimes  called  a  Rheotome, 
and  the  Commutator  or  Current  Keverser,  shown  in  Fig.  136,  is  in  some 
books  called  a  Rheotrope  ;  but  these  terms  are  dropping  out  of  use. 


CHAP,  in  METHODS  OF  USE  196 

209.  Methods    of    Control.  —  In    all    instruments, 
whether  the  moving  part  be  a  magnet  or  a  coil,  some 
controlling  force  is  needful,  otherwise  the  very  smallest 
current  would  turn  the  index  completely  about.    If  small 
currents  are  to  produce  a  small  deflexion,  and  larger  cur- 
rents a  larger,  there  must  be  forces  tending  to  control. 
Several  means  of  control  may  be  used.     These  are  :  — 

(a)  Earth's  Magnetic  Force. — When  the  needle  is  hung 
on  pivot  or  fibre,  the  earth's  magnetic  force  tries  to  bring 
it  back  into  the  magnetic  meridian.  This  is  the  com- 
monest method  in  galvanometers  with  moving  needles. 

(Z>)  Torsion  of  Wire.  —  Moving  part  in  turning  twists 
the  suspending  wire,  which  then  tries  to  untwist,  with  a 
force  which  increases  as  the  angle  of  deflexion.  This 
method  is  commonest  in  galvanometers  with  suspended 
coils. 

(c)  Gravity.  —  If  needle  is  pivoted  on  trunnions  to  move 
in  vertical  plane,  it  may  be  weighted  at  one  end. 

(d)  Permanent  Magnet  Control.  —  To  render  a  needle 
instrument  independent  of  position,  it  may  be  arranged 
with  a  powerful  external  steel  magnet  to  bring  the  needle 
back  to  zero. 

(e)  Bifilar  Suspension.  —  A  needle  or  coil   hung  by 
two  parallel  threads  tends  by  gravity  to  return  to  its 
initial  position. 

To  make  an  instrument  very  sensitive  the  control 
must  be  weakened  as  much  as  possible. 

210.  Methods   of  Observation.  —  There    are    follow- 
ing methods  of  using  galvanometers  in  making  observa- 
tions :  — 

(i.)  Deflexion  Method.  —  The  angle  through  which  the 
moving  part  (whether  needle  or  coil)  is  deflected 
is  read  off  on  a  scale,  by  pointer  or  reflected  beam 
of  light,  when  the  moving  part  has  come  to  rest. 
This  is  the  commonest  method. 

(ii.)  Torsion  Method.  —  The  moving  part  is  suspended 
by  a  wire  from  a  torsion  head,  which  is  turned 


196  ELECTRICITY   AND  MAGNETISM        PART  i 

round  until  the  index  is  brought  back  to  zero ; 
the  controlling  force  then  balancing  the  deflect- 
ing force.  This  very  accurate  method,  due  to 
Ohm,  is  used  in  Siemens'  electrodynamometer 
(Art.  394). 

(iii.)  First  Swing  Method.  —  Instead  of  waiting  for 
moving  part  to  come  to  rest  the  first  siuing  may 
be  observed.  This  method  which  is  the  only 
one  practicable  for  sudden  discharges,  or  for 
transient  currents,  is  called  the  ballistic  method 
(see  Art.  218).  If  the  moving  part  is  riot 
damped  in  its  motion  the  first  swing  on  turn- 
ing on  a  battery  current  is  exactly  twice  the 
angle  at  which  the  deflexion  settles  down. 

(iv.)  Oscillation  Method.  —  Instead  of  observing  deflex- 
ion, the  time  of  oscillation  of  the  needle  may 
be  observed,  the  coil  being  in  this  method  set 
at  right  angles  to  the  magnetic  meridian.  Al- 
lowance must  be  made,  as  in  Art.  133,  for  the 
earth's  magnetism. 

(v.)  Cumulative  Method.  —  For  very  minute  currents 
a  method  is  sometimes  adopted  to  get  up  a 
measurable  swing  by  reversing  the  current  (by 
hand)  as  the  needle  swings  through  zero. 
Sometimes  a  rotating  commutator  of  special 
construction  is  employed  to  produce,  and  accu- 
mulate, the  successive  impulses. 

(vi.)  Null  Methods.  —  In  many  cases  combinations  are 
used  (Wheatstone's  "Bridge,"  "Differential 
Galvanometers,"  etc.)  of  such  a  kind  that  when 
the  conditions  of  electrical  equilibrium  are  at- 
tained no  current  will  flow  through  the  galva- 
nometer in  the  circuit.  Such  methods,  which 
are  generally  exceedingly  accurate,  are  known 
as  null  methods.  For  such  methods  sensitive 
galvanometers  are  applicable,  but  the  gradua- 
tion of  their  scale  is  unimportant. 


CHAP.    Ill 


ASTATIC   GALVANOMETER 


197 


211.  Nobili's  Astatic  Galvanometer.  —  The  instru- 
ment constructed  by  Nobili,  consisting  of  an  astatic  pair 
of  needles  delicately  hung,  so  that  the  lower  one  lay 
within  a  coil  of  wire  wound  upon  an  ivory  frame  (Fig. 
119),  was  for  long  the  favourite  form  of  sensitive  gal- 
vanometer. The  needles  of  this  instrument,  being  inde- 
pendent of  the  earth's  magnetism,  take  their  position  in 
obedience  to  the  torsion  of  the  fibre  by  which  they  are 
hung.  The  frame  on  which  the  coil  is  wound  must  be 
set  carefully  parallel  to  the  needles  ;  and  three  screw  feet 
serve  to  adjust  the 
base  of  the  instru- 
ment level.  Protec- 
tion against  currents 
of  air  is  afforded  by  a 
glass  shade.  When 
a  current  is  sent 
through  the  wire  coils 
the  needles  move  to 
right  or  left  over 
a  graduated  circle. 
When  the  deflexions 
are  small  (i.e.  less  than 
10°  or  15°)  they  are 
very  nearly  propor- 
tional to  the  strength 
of  the  currents  that 


Fig.  119. 


produce  them.  Thus,  if  a  current  produces  a  deflexion 
of  6°  it  is  known  to  be  approximately  three  times  as 
strong  as  a  current  which  only  turns  the  needle  through 
2°.  But  this  approximate  proportion  ceases  to  be  true 
if  the  deflexion  is  more  than  15°  or  20° ;  for  then  the 
needle  is  not  acted  upon  so  advantageously  by  the  cur- 
rent, since  the  poles  are  no  longer  within  the  coils,  but 
are  protruding  at  the  side,  and,  moreover,  the  needle 
being  oblique  to  the  force  acting  on  it,  part  only  of  the 
force  is  turning  it  against  the  directive  force  of  the  fibre ; 


108  ELECTRICITY  AND   MAGNETISM       PART  i 

the  other  part  of  the  force  is  uselessly  pulling  or  pushing 
the  needle  along  its  length.  It  is,  however,  possible  to 
calibrate  the  galvanometer  —  that  is,  to  ascertain  by 
special  measurements,  or  by  comparison  with  a  standard 
instrument,  to  what  strengths  of  current  particular 
amounts  of  deflexion  correspond.  Thus,  suppose  it  once 
known  that  a  deflexion  of  32°  on  a  particular  galva- 
nometer is  produced  by  a  current  of  TJ7  of  an  ampere, 
then  a  current  of  that  strength  will  always  produce  on 
that  instrument  the  same  deflexion,  unless  from  any 
accident  the  controlling  force  has  been  altered. 

212.    The   Tangent    Galvanometer.  —  It  is  not  — for 
the  reasons  mentioned  above  —  possible  to  construct  a 


Fig.  1'2u. 

galvanometer  in  which  the  angle  (as  measured  in  degrees  of 
arc)  through  which  the  needle  is  deflected  is  proportional 
throughout  its  whole  range  to  the  strength  of  the  current. 
But  it  is  possible  to  construct  a  very  simple  galvanometer 


CHAP,  in        TANGENT  GALVANOMETER  199 

in  which  the  tangent  *  of  the  angle  of  deflexion  shall  be 
accurately  proportional  to  the  strength  of  the  current. 
The  essential  feature  of  all  tangent  galvanometers  is  that 
while  the  coil  is  a  large  open  ring  the  needle  is  relatively 
very  small.  Fig.  120  shows  a  form  of  Tangent  Galva- 
nometer suitable  for  large  currents.  The  coil  of  this  in- 
strument consists  of  a  simple  circle  of  stout  copper  wire 
from  10  to  15  inches  in  diameter.  Other  tangent  gal- 
vanometers have  many  turns  of  fine  wire  wound  upon 
a  large  open  ring.  At  the  centre  is  delicately  suspended 
a  magnetized  steel  needle  not  exceeding  1  inch  in  length, 
and  usually  furnished  with  a  light  index  of  aluminium. 
The  instrument  is  adjusted  by  setting  the  coil  in  the 
magnetic  meridian,  the  small  needle  lying  then  in  the 
plane  of  the  coil. 

The  "  field  "  due  to  a  current  passing  round  the  circle 
is  very  uniform  at  and  near  the  centre,  and  the  lines  of 
force  are  there  truly  normal  to  the  plane  of  the  coil. 
This  is  not  true  of  other  parts  of  the  space  inside  the 
ring,  the  force  being  neither  uniform  nor  normal  in  direc- 
tion, except  centrally  in  the  plane  of  the  coil  and  along 
the  axis.  The  needle  being  small,  its  poles  are  never 
far  from  the  centre,  and  hence  never  protrude  into  the 
regions  where  the  field  is  irregular. f  Whatever  mag- 
netic force  the  current  in  the  coil  can  exert  on  the  needle 
is  exerted  normally  to  the  plane  of  the  ring,  and  there- 
fore at  right  angles  to  the  magnetic  meridian.  As  the 
two  forces  — that  due  to  the  current  and  that  due  to  the 
controlling  magnetism  of  the  earth  —  act  squarely  to  one 


*  See  note  on  Ways  of  Reckoning  Angles,  p.  133. 

t  In  order  to  ensure  uniformity  of  field,  Gaugain  proposed  to  hang  the 
needle  at  a  point  on  the  axis  of  the  coil  distant  from  its  centre  by  a  distance 
equal  to  half  the  radius  of  the  coils.  Helmholtz's  arrangement  of  two 
parallel  coils,  symmetrically  set  on  either  side  of  the  needle,  is  better ;  and 
a  three-coil  galvanometer,  having  the  central  coil  larger  than  the  others,  so 
that  all  three  may  lie  in  the  surface  of  a  sphere  having  the  small  needle  at 
its  centre,  is  the  best  arrangement  of  all  for  ensuring  that  the  field  at  the 
centre  is  uniform. 


200 


ELECTRICITY  AND   MAGNETISM       PART  i 


another,  the  action  of  the  current  will  not  be  measured 
by  equal  degrees  marked  out  around  a  circle,  but  will  be 
measured  by  equal  divisions  along  a  tangent  line,  as 
shown  below.  Now,  it  was  proved  in  Art.  137  that 
the  magnetic  force  which,  acting  at  right  angles  to  the 
meridian,  produces  on  a  magnetic  needle  the  deflexion  5 
is  equal  to  the  horizontal  force  of  the  earth's  magnetism 
at  that  place  multiplied  by  the  tangent  of  the  angle  of 
deflexion.  Hence  a  current  flowing  in  the  coil  will  turn 
the  needle  aside  through  an  angle  such  that  the  tangent  of 
the  angle  of  deflexion  is  proportional  to  the  strength  of  the 
current. 

Example. — Suppose  a  certain  battery  gave  a  deflexion  of 
15°  on  a  tangent  galvanometer,  and  another  battery 
yielding  a  stronger  current  gave  a  deflexion  of  30°.  The 
strengths  currents  are  not  in  the  proportion  of  15 :  30, 
but  in  the  proportion  of  tan  15°  to  tan  30°.  These 
values  must  be  obtained  from  a  table  of  natural  tan- 
gents like  that  given  in  Appendix  A,  from  which  it  will 
be  seen  that  the  ratio  between  the  strengths  of  the  cur- 
rents is  -268:  '577,  or  about  10:  22. 

Or,  more  generally,  if  current  C  produces  deflexion  fi,  and 
current  C'  deflexion  &',  then 

C  ;  C  =  tan  5 :  tan  5' 

To  obviate  reference  to  a  table  of  figures,  the  circular 
scale  of   the   instrument  is  sometimes  graduated   into 


Fip.  121. 

tangent   values   instead    of    being    divided    into    equal 
degrees  of  arc.     Let  a  tangent  OT   be   drawn   to  the 


CHAP,  in  TANGENT   SCALES  201 

circle,  as  in  Fig.  121,  and  along  this  line  let  any  num- 
ber of  equal  divisions  be  set  off,  beginning  at  O.  From 
these  points  draw  back  to  the  centre.  The  circle  will 
thus  be  divided  into  a  number  of  pieces,  of  which  those 
near  O  are  nearly  equal,  but  which  get  smaller  and 
smaller  away  from  O.  These  unequal  pieces  correspond 
to  equal  increments  of  the  tangent.  If  the  scale  were 
divided  thus,  the  readings  would  be  proportional  to  the 
tangents.  It  is,  however,  harder  to  divide  an  arc  into 
tangent  lines  with  accuracy  than  to  divide  it  into  equal 
degrees ;  hence  this  graduation,  though  convenient,  is  not 
used  where  great  accuracy  is  needed. 

213.  Absolute  Measure  of  Current  by  Tangent  Gal- 
vanometer. —  The  strength  of  a  current  may  be  deter- 
mined in  "  absolute  "  units  by  the  aid  of  the  tangent 
galvanometer  if  the  "  constants  "  of  the  instrument  are 
known.  The  tangent  of  the  angle  of  deflexion  repre- 
sents (see  Art.  137)  the  ratio  between  the  magnetic  force 
due  to  the  current  and  the  horizontal  component  of  the 
earth's  magnetic  force.  Both  these  forces  act  on  the 
needle,  and  depend  equally  upon  the  magnetic  moment 
of  the  needle,  which,  therefore,  we  need  not  know  for 
this  purpose.  We  know  that  the  force  exerted  by  the 
current  at  centre  of  the  coil  is  proportional  to  the 
horizontal  force  of  the  earth's  magnetism  multiplied 
by  the  tangent  of  the  angle  of  deflexion.  These  two 
quantities  can  be  found  from  the  tables,  and  from  them 
we  calculate  the  absolute  value  of  the  current  as  fol- 
lows :  —  Let  r  represent  the  radius  of  the  galvanometer 
coil  (measured  in  centimetres)  ;  its  total  length  (if  of  one 
turn  only)  is  2  irr.  The  distance  from  the  centre  to  all 
parts  of  the  coil  is  of  course  r.  From  our  definition 
of  the  unit  of  strength  of  current  (Art.  207),  it  follows 

that  C  x  "^-  —  force  (in  dynes)  at  centre, 

or  Cx^T  =  H-tan8; 


202  ELECTRICITY   AND   MAGNETISM        PART  i 

hence  C  =  —  •  H  •  tan  8. 

—  7T 

The  quantity  27r/r,  or  2irn/r  if  the  coil  has  n  turns, 
is  sometimes  called  the  "  constant "  or  the  "  principal 
constant "  of  the  galvanometer  and  denoted  by  the  sym- 
bol G.  Hence  the  value  of  the  current  in  absolute 
(electromagnetic)  units  *  will  be  expressed  as 

C  =  ?  .  tan  8. 
G 

The  constant  G  represents  the  strength  of  field  pro- 
duced at  the  centre  of  the  coil  by  unit  current. 

214.  Sine  Galvanometer.  —  The  disadvantage  of 
the  tangent  galvanometer  just  described  is  that  it  is  not 
very  sensitive,  because  the  coil  is  necessarily  very  large 
as  compared  with  the  needle,  and  therefore  far  away 
from  it.  A  galvanometer  with  a  smaller  coil  or  a  larger 
needle  could  not  be  used  as  a  tangent  galvanometer, 
though  it  would  be  more  sensitive.  Any  sensitive 
galvanometer  in  which  the  needle  is  directed  by  the 
earth's  magnetism  can,  however,  be  used  as  a  Sine 
Galvanometer,  provided  the  frame  on  which  the  coils 
are  wound  is  capable  of  being  turned  round  a  central 
axis.  When  the  instrument  is  so  constructed,  the  fol- 
lowing method  of  measuring  currents  is  adopted.  The 
coils  are  first  set  parallel  to  the  needle  {i.e.  in  the  mag- 
netic meridian) ;  the  current  is  then  sent  through  it, 
producing  a  deflexion;  the  coil  itself  is  rotated  round 
in  the  same  sense,  and,  if  turned  round  through  a  wide 
enough  angle,  will  overtake  the  needle,  which  will  once 
more  lie  parallel  to  the  coil.  In  this  position  two  forces 
are  acting  on  the  needle :  the  directive  force  of  the  earth's 
magnetism  acting  along  the  magnetic  meridian,  and  the 
force  due  to  the  current  passing  in  the  coil,  which  tends 
to  thrust  the  poles  of  the  needle  out  at  right  angles ; 

*  The  student  will  remember  (Arts.  207  and  354)  that  the  practical  unit 
of  current  which  we  call  "  one  ampere"  is  only  ^  of  one  "  absolute  "  unit 
of  the  centimetre-gramme-second  system. 


CHAP,  in          MIRROR   GALVANOMETER  203 

in  fact  there  is  a  "  couple  "  which  exactly  balances  the 
"  couple "  due  to  terrestrial  magnetism.  Now  it  was 
shown  in  the  Lesson  on  the  Laws  of  Magnetic  Force 
(Art.  136)  that  when  a  needle  is  deflected  the  u  moment " 
of  the  couple  is  proportional  to  the  sine  of  the  angle  of 
deflexion.  Hence  in  the  sine  galvanometer,  when  the 
coil  has  been  turned  round  so  that  the  needle  once  more 
lies  along  it,  the  strength  of  the  cm-rent  in  the  coil  is  pro- 
portional to  the  sine  of  the  angle  through  ichich  the  coil  has 
been  turned.* 

215.  The  Mirror  Galvanometer. — When  a  galva- 
nometer of  great  delicacy  is  needed,  the  moving  parts 
must  be  made  very  light  and  small.  To  watch  the  move- 
ments of  a  very  small  needle  an  index  of  some  kind  must 
be  used;  indeed,  in  the  tangent  galvanometer  it  is  usual  to 
fasten  to  the  short  stout  needle  a  delicate  stiff  pointer  of 
aluminium.  A  far  better  method  is  to  fasten  to  the 
needle  a  very  light  mirror  of  silvered  glass,  by  means  of 
which  a  beam  of  light  can  be  reflected  on  to  a  scale,  so 
that  every  slightest  motion  of  the  needle  is  magnified 
and  made  apparent.  The  mirror  galvanometers  devised  by 
Sir  W.  Thomson  (Lord  Kelvin)  for  signalling  through 
submarine  cables,  are  admirable  examples  of  this  class  of 
instrument.  In  Fig.  122  the  general  arrangements  of  this 
instrument  are  shown.  The  body  of  the  galvanometer, 
consisting  of  a  bobbin  on  which  is  wound  the  coil,  is  sup- 

*  Again  the  student  who  desires  to  compare  the  strength  of  two  cur- 
rents will  require  the  help  of  a  table  of  natural  sines,  like  that  given  in 
Appendix  A.  Suppose  that  with  current  C  the  coils  had  to  be  turned 
through  an  angle  of  6  degrees ;  and  that  with  a  different  current  C '  the 
coils  had  to  be  turned  through  &'  degrees,  then 

C  :  C'  =  sin  6:  sm0'. 

It  is  of  course  assumed  that  the  instrument  is  provided  with  a  scale  of 
degrees  on  which  to  read  off  the  angle  through  which  the  coils  have  been 
turned.  It  is  possible  here  also,  for  rough  purposes,  to  graduate  the  circle 
not  in  degrees  of  arc,  but  in  portions  corresponding  to  equal  additional 
values  of  the  sine.  The  student  should  try  this  way  of  dividing  a  circle 
after  reading  the  note  On  Ways  of  Reckoning  Angles,  p.  138. 


204 


ELECTRICITY   AND   MAGNETISM       PART  i 


ported  011  three  screw  feet  by  which  it  can  be  adjusted. 
The  magnet  consists  of  one  or  more  small  pieces  of  steel 
watch-spring  attached  to  the  back  of  a  light  concave  sil- 
vered glass  mirror  about  as  large  as  a  threepenny  piece, 
weighing  altogether  only  two  or  three  grains.  This  mir- 
ror is  hung  by  a  single  fibre  of  cocoon  silk  within  the 
coil,  and  a  curved  magnet,  which  serves  to  counteract  the 


Fig.  122. 

magnetism  of  the  earth,  or  to  direct  the  needle,  is  carried 
upon  a  vertical  support  above.  Another  view  of  the  sus- 
pended mirror  and  magnets  is  shown  in  Fig.  123.  Oppo- 
site the  galvanometer  is  placed  the  scale.  A  beam  of 
light  from  a  paraffin  lamp  passes  through  a  narrow  aper- 
ture under  the  scale  and  falls  on  the  mirror,  which  reflects 
it  back  on  to  the  scale.  The  mirror  is  slightly  concave, 
and  gives  a  well-defined  spot  of  light  if  the  scale  is 
adjusted  to  suit  the  focus  of  the  mirror.  The  adjusting 
magnet  enables  the  operator  to  bring  the  reflected  spot  of 


CHAP,  in      SENSITIVE  GALVANOMETERS 


205 


light  to  the  zero  point  at  the  middle  of  the  scale.  The 
feeblest  current  passing  through  the  galvanometer  will 
cause  the  spot  of  light  to  shift  to  right  or  left.  The  tiny 
current  generated  by  dipping  into  a  drop  of  salt  water 
the  tip  of  a  brass  pin  and  a  steel  needle  (connected  by 
wires  to  the  terminals  of  the  galvanometer)  will  send  the 
spot  of  light  swinging  right  across  the  scale.  If  a  pow- 
erful limelight  is  used,  the  movement  of  the  needle  can 
be  shown  to  a  thousand  persons  at  once.  For  still  more 
delicate  work  an  astatic  pair  of  needles  can  be  used,  each 


Fig.  123. 


Fig.  124. 


being  surrounded  by  its  coil,  and  having  the  mirror  rig- 
idly attached  to  one  of  the  needles.  Such  a  form,  with 
two  bobbins,  wound  so  as  to  be  traversed  by  the  current 
in  opposite  senses,  is  represented  diagrammatically  in  Fig. 
124.  Such  an  instrument,  made  with  four  bobbins,  two 
in  front  and  two  behind  the  suspended  needle  system,  and 
having  on  each  bobbin  about*  miles  of  a  wire  about 
T^  inch  in  thickness,  insulated  by  a  coating  of  silk,  is 
capable  of  showing  by  a  deflexion  of  one  division  on  its 
scale  an  excessively  minute  current,  even  down  to  one 
fifty-four  thousand  millionth  part  of  one  ampere. 

216.  Suspended  Coil  Galvanometers.  —  These  have 
been  used  by  Sturgeon  (1836),  Varley  (1860),  and  others, 
and  the  principle  was  also  applied  in  Lord  Kelvin's 


206 


ELECTRICITY   AND   MAGNETISM       PART  i 


Fig.  125. 


"  Siphon  Recorder."     The  best  known  is  that  of  D'Arson- 

val  depicted  in  Fig.  125.  Between  the  poles  of  a 
compound  permanent  steel  magnet  of 
U- shape  is  suspended  by  very  thin 
hard-drawn  silver  wires  an  open  coil  of 
mirror  very  fine  wire  wound  on  a  light  rec- 
tangular frame.  The  current  is  led  to 
and  from  the  coil  by  the  suspending 
wires.  Within  the  suspended  coil  is  a 
cylinder  of  soft  iron,  supported  from 
behind,  to  concentrate  the  magnetic 
field.  The  vertical  parts  of  the  coil 
then  hang  freely  in  the  two  narrow 
gaps  where  the  magnetic  field  is  very 
intense.  The  force  tending  to  turn  the 
coil  is  proportional  to  the  current,  to 
the  number  of  windings,  and  to  the 

intensity  of  the  magnetic  field,  so  that  by  making  the 

magnet  very  powerful  the  instrument 

becomes  very  sensitive .  The  elasticity 

of  the  suspending  wires  controls  the 

position  of  the  coil  and  tends  to  bring 

it  back  to  its  initial  position.    These 

galvanometers  are  independent  of  the 

earth's  magnetic  field,  and  are  not 

affected  by  magnets  in  their  neigh- 
bourhood, so  that  they  can  be  used 

in  many  places  where  other  galva- 
nometers could  not.     They  are  also 

remarkably  dead-beat.*  Some   are 

provided    with     a    pointer    and    a 

horizontal  dial ;  others  more  usually 

have  a  mirror  attached  to  the  coil 

to  reflect  a  spot  of  light. 

Most  recent  is  the  suspended-coil 

galvanometer  of  Ayrton  and  Mather  (Fig.  126).   Here  the 

suspended  coil  is  formed  as  an  elongated  loop  with  no 


CHAP,  in        SPECIAL  GALVANOMETERS  207 

aperture  between  its  sides.  Consequently  the  poles  of 
the  magnets  may  be  brought  very  close  together;  and 
these  are  made  up  of  a  number  of  flat  steel  magnets  of 
nearly  circular  form  piled  up  on  one  another.  One  of 
these  instruments,  with  mirror  and  scale,  will  show  a 
deflexion  of  one  scale  division,  with  a  current  less  than 
one  ninety-millionth  part  of  1  ampere. 

Strong  currents  must  not  be  passed  through  very  sen- 
sitive galvanometers,  for,  even  if  they  are  not  spoiled,  the 
deflexions  of  the  needle  will  be  too  large  to  give  accurate 
measurements.  In  such  cases  the  galvanometer  is  used 
with  a  shunt,  or  coil  of  wire  arranged  so  that  the  greater 
part  of  the  current  shall  flow  through  it,  and  pass  the  gal- 
vanometer by,  only  a  small  portion  of  the  current  actually 
traversing  the  coils  of  the  instrument.  The  resistance 
of  the  shunt  must  bear  a  known  ratio  to  the  resistance  of 
the  instrument,  according  to  the  principle  laid  down  in 
Art.  409  about  branched  circuits. 

217-  Differential  Galvanometer.  —  For  the  purpose 
of  comparing  two  currents  a  galvanometer  is  sometimes 
employed,  in  which  the  coil  consists  of  two  separate  wires 
wound  side  by  side.  If  two  equal  currents  are  sent  in 
opposite  directions  through  these  wires,  the  needle  will 
not  move.  If  the  currents  are,  however,  unequal,  then 
the  needle  will  be  moved  by  the  stronger  of  them,  with 
an  intensity  corresponding  to  the  difference  of  the 
strengths  of  the  two  currents. 

218.  Ballistic  Galvanometer.  —  In  order  to  measure 
the  strength  of  currents  which  last  only  a  very  short  time, 
galvanometers  are  employed  in  which  the  needle  takes  a 
relatively  long  time  to  swing.  This  is  the  case  with  long 
or  heavy  needles ;  or  the  needles  may  be  weighted  by 
enclosing  them  in  leaden  cases.  As  the  needle  swings 
slowly  round,  it  adds  up,  as  it  were,  the  varying  impulses 
received  during  the  passage  of  a  transient  current.  The 
sine  of  half  the  angle  of  the  first  swing  is  proportional  to  the 
quantity  of  electricity  that  has  flowed  through  the  coil.  The 


208  ELECTRICITY   AND   MAGNETISM        PART  i 

charge  of  a  condenser  may  thus  be  measured  by  discharg- 
ing it  through  a  ballistic  galvanometer  (see  Art.  418&). 
The  needle  must  not  be  damped. 

219.  Methods  of  Damping :  Aperiodic  Galvano- 
meters.—  To  prevent  the  needle  from  swinging  to  and 
fro  for  a  long  time  devices  are  used  to  damp  the  motion. 
These  are :  — 

(a)  Air  Damping.  —  A  light  vane  attached  to  needle 
beats  against  the  air  and  damps  the  motion.  In  mirror 
instruments  the  mirror  itself  damps,  particularly  if  con- 
fined in  a  narrow  chamber. 

(£>)    Oil  Damping.  — A  vane  dips  into  oil. 

(c)  Magnetic  Damping.  —  If  the  needle  swings  close 
to  or  inside  a  mass  of  copper,  it  will  soon  come  to  rest  by 
reason  of  the  eddy-currents  (Art.  457)  induced  in  the 
copper.  Eddy-currents  damp  the  motion  of  the  suspended 
coil  in  instruments  of  that  class. 

The  period  of  swing  can  be  reduced  by  diminishing 
the  weight  and  leverage  of  the  moving  parts  so  as  to 
lessen  their  moment  of  inertia.  It  can  also  be  lessened 
(at  the  expense  of  the  sensitiveness  of  the  instrument) 
by  increasing  the  controlling  forces.  An  instrument  so 
well  damped  as  to  come  to  rest  without  getting  up  a 
periodic  swing  is  called  an  aperiodic  or  dead-beat  instru- 
ment. 

12O.  Voltmeters,  or  Potential  Galvanometers.  —  If  any 
galvanometer  be  constructed  with  a  very  long  thin  wire 
of  high  resistance  as  its  coil,  very  little  current  will  flow 
through  it,  but  what  little  current  flows  will  be  exactly 
proportional  to  the  potential  difference  that  may  be 
applied  to  the  two  ends  of  its  circuit.  Such  a  galvano- 
meter, suitably  provided  with  a  scale,  will  indicate  the 
number  of  volts  between  its  terminals.  Many  forms  of 
voltmeter-galvanometers  exist,  but  they  all  agree  in  the 
essential  of  having  a  coil  of  a  high  resistance  —  sometimes 
several  thousand  ohms.  The  suspended-coil  galvano- 
meters described  in  Art.  21G  make  excellent  voltmeters. 


CHAP.    Ill 


AMPEREMETERS 


Weston's  voltmeter,  largely  used  in  America,  is  of  this 
class,  the  coil  being  delicately  pivoted,  and  controlled  by 
a  spiral  spring.  Any  sensitive  mirror  galvanometer  can 
be  used  as  a  voltmeter  by  simply  adding  externally  to  its 
circuit  a  resistance  sufficiently  great.  There  are  also 
other  voltmeters  that  depend  on  electrostatic  actions; 
they  are  a  species  of  electrometer  and  are  described  in  Art. 
290.  Cardew's  voltmeter  (see  Art.  430)  differs  from  the 
above  class  of  instrument,  and  consists  of  a  long  thin 
platinum  wire  of  high  resistance,  which  expands  by  heat- 
ing when  it  is  connected  across  a  circuit.  All  voltmeters 
are  placed  as  shunts  across  between  the  two  points  the 
potential  difference  of  which  is  to  be  measured.  They 
are  never  joined  up  in  circuit  as  amperemeters  are. 

221.  Amperemeters,  or  Ammeters.  —  A  galvanometer 
graduated  so  that  its  index  reads  directly  on  the  scale 
the  number  of  amperes  (Art.  207) 
flowing  through  the  coil  is  called  an 
Amperemeter.  Such  instruments  were 
introduced  in  form  for  industrial  use 
in  1870  by  Ayrton  and  Perry.  Many 
other  forms  were  subsequently  in- 
vented. In  Ayrton  and  Perry's  in- 
struments (Fig.  127),  which  are 
portable  and  "  dead-beat  "  in  action, 
the  needle,  which  is  oval  in  shape,  is 
placed  between  the  poles  of  a  power- 
ful permanent  magnet  to  control  its 
direction  and  make  it  independent 
of  the  earth's  magnetism.  By  a  peculiar  shaping  of  the 
pole-pieces,  needle,  and  coils,  the  angular  deflexions  are 
proportional  to  the  strength  of  the  deflecting  current. 
These  amperemeters  are  made  with  short  coils  of  very 
low  resistance  and  few  turns  of  wire.  Ayrton  and  Perry 
also  arranged  voltmeters  (Art.  220)  in  a  similar  form,  but 
with  long  coils  of  high  resistance. 

Among  the   innumerable  forms  of  amperemeter  in 


210  ELECTRICITY   AND   MAGNETISM        PART  i 

commerce  there  are  a  number  in  which  there  is  neither 
magnet   nor  iron,  but  which   depend  upon  the  mutual 
force  between  a  fixed  and  a  movable  coil  traversed  by 
the  current.     These  are  dealt  with  in 
Art.  394,  and  are  suitable  for  alternate 
currents  as  well  as  continuous  currents. 
Of  this  kind  are  Siemens'  electrodyna- 
mometer  and  the  Kelvin  balances. 

Other  instruments  depend  upon  the 
magnetic  properties  of  iron  under  the 
influence  of  the  current.     Of  this  class 
Fig"l28  are  ^ie   Schuckert  instruments  repre- 

sented in  Fig.  128.  An  index  pivoted 
in  the  axis  of  an  open  coil  carries  a  light  strip  of  soft 
iron  seen  endways  at  B.  Another  strip  A  is  fixed  within 
the  coil.  The  current  flowing  round  the  coil  magnetizes 
these  strips  and  they  repel  one  another.  Gravity  is  here 
the  controlling  force. 

LESSON  XVIII. —  Currents  produced  by  Induction 

222.  Faraday's  Discovery.  —  In  1831  Faraday  dis- 
covered that  currents  can  be  induced  in  a  closed  circuit 
by  moving  magnets  near  it,  or  by  moving  the  circuit 
across  the  magnetic  field ;  and  he  followed  up  this  dis- 
covery by  finding  that  a  current  whose  strength  is  chang- 
ing may  induce  a  secondary  current  in  a  closed  circuit 
near  it.  Such  currents,  whether  generated  by  magnets 
or  by  other  currents,  are  known  as  Induction  Currents. 
And  the  action  of  a  magnet  or  current  in  producing 
such  induced  currents  is  termed  electromagnetic  (or 
magneto-electric)  induction,*  or  simply  induction.  Upon 

*  The  student  must  not  confuse  this  electromagnetic  induction  with 
the  phenomenon  of  the  electrostatic  induction  of  one  charge  of  electricity 
by  another  charge,  as  explained  in  Lesson  III.,  and  which  has  nothing-  to 
do  with  currents.  Formerly,  before  the  identity  of  the  electricity  derived 
from  different  sources  was  understood  (Art.  24G),  electricity  derived  thus 


CHAP,  in     MAGNETO-ELECTRIC   INDUCTION  211 

this  principle  are  based  the  modern  dynamo  machines 
for  generating  electric  currents  mechanically,  as  well  as 
induction  coils,  alternate-current  transformers,  and  other 
appliances. 

223.  Induction  of  Currents  by  Magnets.  —  If  a  coil 
of  insulated  wire  be  connected  in  circuit  with  a  suffi- 
ciently delicate  galvanometer,  and  a  magnet  be  inserted 
rapidly  into  the  hollow  of  the  coil  (as  in  Fig.  129),  a 
momentary  current  is  observed 
to  flow  round  the  circuit  while 
the  magnet  is  being  moved 
into  the  coil.  So  long  as  the 
magnet  lies  motionless  in  the 
coil  it  induces  no  currents. 
But  if  it  be  rapidly  pulled  out 
of  the  coil  another  momentary 
current  will  be  observed  to 
flow,  and  in  the  opposite 
direction  to  the  former.  The 
induced  current  caused  by 
inserting  the  magnet  is  an  £; 
inverse  current,  or  is  in  the  Jl 
opposite  direction  to  that  C^^iH 
which  would  magnetize  the  V]s- 

magnet  with  its  existing  polarity.  The  induced  current 
caused  by  withdrawing  the  magnet  is  a  direct  current. 

Precisely  the  same  effect  is  produced  if  the  coil  be 
moved  towards  the  magnet  as  if  the  magnet  were  moved 
toward  the  coil.  The  more  rapid  the  motion  is,  the 
stronger  are  the  induced  currents. 

The  magnet  does  not  grow  any  weaker  by  being  so 
used,  for  the  real  source  of  the  electrical  energy  generated 
is  the  mechanical  energy  spent  in  the  motion. 

from  the  motion  of  magnets  was  termed  magneto-electricity.  For  most 
purposes  the  adjectives  magneto-electric  and  electro-magnetic  are  synony- 
mous. The  production  of  electricity  from  magnetism,  and  of  magnetism 
from  electricity,  are,  it  is  true,  two  distinct  operations  ;  but  both  are 
included  in  the  branch  of  science  denominated  Electromagnetics. 


212 


ELECTRICITY   AND   MAGNETISM        PARTI 


If  the  circuit  is  not  closed,  no  currents  are  produced  ; 
but  the  relative  motion  of  coil  and  magnet  will  still  set 
up  electromotive-forces,  tending  to  produce  currents. 

Faraday  discovered  these  effects  to  be  connected  with 
the  magnetic  field  surrounding  the  magnet.  lie  showed 
that  no  effect  was  produced  unless  the  circuit  cut  across 
the  invisible  magnetic  lines  of  the  magnet. 

224.  Induction  of  Currents  by  Currents.  —  Faraday 
also  showed  that  the  approach  or  recession  of  a  current 
might  induce  a  current  in  a  closed  circuit  near  it.  This 
may  be  conveniently  shown  as  an  experiment  by  the 
apparatus  of  Fig.  130. 

A  coil  of  insulated  wire  P  is  connected  in  circuit  with 
a  battery  B  of  two  or  three  cells,  and  a  key  K  to  turn  the 


Fig.  130. 

current  on  or  off.  A  second  coil  S,  entirely  unconnected 
with  the  first,  is  joined  up  with  wires  to  a  sensitive  gal- 
vanometer G.  We  know  (Art.  202)  that  a  coil  of  wire 
in  which  a  current  is  circulating  acts  like  a  magnet. 
And  we  find  that  if  while  the  current  is  flowing  in  P, 
the  coil  is  suddenly  moved  up  toward  S,  a  momentary 
current  will  be  induced  in  S.  If  P  is  suddenly  moved 
away  from  S  another  momentary  current  will  be  observed 
in  the  second  circuit.  The  first  of  these  two  momentary 
currents  is  an  "  inverse "  one,  while  the  second  one  is 


CHAP,  in         INDUCTION  OF   CURRENTS 


213 


found  to  be  a  "  direct "  one  (i.e.  one  which  runs  the  same 
way  round  the  coil  S  as  the  battery  current  runs  round 
the  coil  P).  The  coil  P  is  called  the  primary  coil,  and 
the  current  in  it  the  primary  current.  The  other  coil  S 
is  called  the  secondary  coil,  and  the  momentary  currents 
induced  in  it  are  sometimes  called  secondary  currents. 

Let  P  now  be  placed  close  to  S,  no  current  flowing 
in  either  coil.  Then  on  pressing  the  key  K  to  turn  on 
the  primary  current,  it  will  be  noticed  that  during  the 
moment  while  the  current  in  P  is  growing  there  will 
be  a  transient  inverse  current  in  S.  The  effect  of  turn- 
ing on  the  current  is  just  as  if  the  current  had  been 
turned  on  while  P  was  far  away  and  then  P  suddenly 
brought  up  to  S.  Breaking  the  battery  circuit  while  the 
primary  coil  lies  close  to  the  secondary  coil  produces  the 
same  effect  as  if  the  primary  coil  were  suddenly  removed 
to  an  infinite  distance.  Making  the  battery  circuit  while 
the  primary  coil  lies  close  to  the  secondary  produces  the 
same  effect  as  bringing  it  up  suddenly  from  a  distance. 

So  long  as  a  steady  current  traverses  the  primary  cir- 
cuit there  are  no  induced  currents  in  the  secondary  circuit, 
unless  there  is  relative  motion  between  the  two  circuits ; 
but  moving  the  secondary  circuit  towards  the  primary 
has  just  the  same  effect  as  moving  the  primary  circuit 
towards  the  secondary,  and  vice  versa. 

We  may  tabulate  these  results  as  follows  :  — 


By 
means 
of 

Momentary  Inverse 
currents  are  induced 
in  the  secondary  circuit 

Momentary  Direct 
currents  are  induced 
in  the  secondary  circuit 

Magnet 

while  approaching. 

while  receding. 

Current 

while  approaching, 
or  beginning, 
or  increasing  in  strength. 

while  receding, 
or  ending, 
or  decreasing  in  strength. 

214  ELECTRICITY   AND   MAGNETISM        PART  i 

225.    Fundamental  Laws  of   Induction.  —  When  we 

reflect  that  every  circuit  traversed  by  a  current  has  a 

magnetic  field  of  its  own  in  which  there  are  magnetic  lines 

running  through  the  circuit  (Arts.  202  and  389),  we  shall 

see  that  the  facts  tabulated  in  the  preceding  paragraph 

may  be  summed  up  in  the  following  fundamental  laws  :  — 

(i.)  A  decrease  in  the  number  of  lines  which  pass  through 

a   circuit  induces  a  current  round  the  circuit  in 

the  positive    direction  (i.e.  produces  a  "  direct " 

current) ;  while  an  increase  in  the  number  of  lines 

ivhich  pass  through  the  circuit  induces  a  current 

in  the  negative  direction  round  the  circuit  (i.e.  an 

"inverse"  current}. 

Here  we  suppose  the  positive  direction  along  lines  to 

be  the  direction  along  which  a  free  N  pole  would  tend  to 

move,   and   the  positive   direction   of  the   current  that 

which  the  current  must  flow  to  increase  the  magnetic 

flux.     Compare  the  "  corkscrew  "  rule  given  on  p.  183. 

(ii.)    The  total  induced  electromotive-force  acting  round 

a  closed  circuit  is  equal  to  the  rate  of  decrease  in 

the  number  of  lines  which  pass  through  the  circuit. 

Suppose  at  first  the  number  of  magnetic  lines  (Art. 

119)  passing  through  the  circuit  to  be  Np  and  that  after 

a  very  short  interval  of  time  t  the  number  becomes  N2, 

the  averae  induced  electromotive-force  E  is 


t 
By  Ohm's  law,  C  =  E  -  R, 

therefore  C  =    *~.  *• 

If  N2  is  greater  than  Nv  and  there  is  an  increase  in  the 
number  of  lines,  then  Nl  —  N2  will  be  a  negative  quantity, 
and  C  will  have  a  negative  sign,  showing  that  the  E.M.F. 
is  an  inverse  one.  A  coil  of  50  turns  of  wire  cutting 
1000  lines  will  produce  the  same  effect  as  a  coil  of  5 


CHAP,  in        CUTTING   MAGNETIC   LINES  215 


10,000  lines,  or  of    1  turn  cutting  50,000 
lines. 

To  induce  an  electromotive-force  equal  to  that  of  a 
single  DanielFs  cell  would  require  that  110,000,000  lines 
should  be  cut  in  one  second.  As  such  large  numbers 
are  inconvenient  to  express  the  facts,  the  unit  of  E.M.F., 
the  volt,  has  been  chosen  to  correspond  to  the  cutting  of 
100,000,000  lines  per  second. 

Example.  —  Suppose  the  number  of  magnetic  lines  to  dimin- 
ish from  800,000  to  0  m  the  ^  of  a  second,  the  rate  of 
diminution  is  40,000,000  lines  per  second.  And  since 
1  volt  is  taken  as  108  lines  per  second,  the  average  in- 
duced E.M.F.  during  that  time  will  be  0'4  volt; 

A  reference  to  Fig.  176  will  make  this  important  law 
clearer.  Suppose  ABCD  to  be  a  wire  circuit  of  which  the 
piece  AB  can  slide  along  DA  and  CB  towards  S  and  T. 
Let  the  vertical  arrows  represent  vertical  lines  of  force  in 
a  uniform  magnetic  field,  and  show  (as  is  the  case  with 
the  vertical  components  of  the  earth's  lines  of  force  in  the 
northern  hemisphere)  the  direction  in  which  a  N-pointing 
pole  would  move  if  free.  The  positive  direction  of  these 
magnetic  lines  is  therefore  vertically  downwards  through 
the  circuit.  Now  if  AB  slide  towards  ST  with  a  uniform 
velocity  it  will  cut  a  certain  number  of  lines  every  second, 
and  a  certain  number  will  be  added  during  every  second 
of  time  to  the  total  number  passing  through  the  circuit. 
If  Nj  be  the  number  at  the  beginning,  and  N2  that  at 
the  end  of  a  circuit,  N\  —  N2  will  be  a  negative  quantity, 
and  there  will  be  generated  an  electromotive-force  whose 
direction  through  the  sliding  piece  is  from  A  towards  B. 

It  is  important  to  note  that  all  these  inductive  opera- 
tions are  really  magnetic.  In  the  experiment  with  the 
two  coils  P  and  S  it  is  the  magnetic  lines  of  coil  P  which 
pass  through  coil  S  and  set  up  the  induced  E.M.F.  This 
is  proved  by  the  following  further  experiment.  Take  a 
bar  of  iron  —  a  poker,  or  better  still,  a  bundle  of  iron 
wires  —  and  lay  it  along  the  dotted  line  so  that  its  ends 


216 


ELECTRICITY   AND   MAGNETISM        PART  i 


pass  through  P  and  S.  It  will  by  its  great  magnetic  per- 
meability help  to  conduct  the  magnetic  lines  from  P 
through  S.  And  when  it  is  so  placed  it  will  be  found 
greatly  to  intensify  the  actions.  In  fact  if  P  is  many 
inches  away  from  S,  and  the  iron  core  is  present,  the 
inductive  effects  of  turning  the  current  on  and  off  may 
be  as  great  as  if,  in  the  absence  of  the  core,  P  were 
pushed  up  close  to  S. 

226.  Direction  of  Induced  E.M.F.  —  It  is  convenient 
to   have   rules  for  remembering  the  relations  in  direc- 
tion between    the   magnetism,  the  motion,  and  the  in- 
duced    electromotive -force. 
Of  such  rules  the  following, 
due  to  Fleming,  is  most  use- 
ful :  Let  the  forefinger  of  the 

fX  right  hand  (Fig.  131)  point  in 
the  direction  of  the  magnetic 
lines;  then  turn  the  thumb  in 
the  direction  of  the  motion  :  the 
middle  finger  bent  at  right 
angles  to  both  thumb  and  fore- 
finger will  show  the  direction  of 
the  induced  E.M.F. 

Another  often  given  is  an 

adaptation  of  Ampere's  rule :  Suppose  a  figure  swimming 
in  any  conductor  to  turn  so  as  to  look  along  the  (positive 
direction  of  the)  lines,  then  if  he  and  the  conductor  be  moved 
towards  his  right  hand  he  will  be  swimming  with  the  current 
induced  by  this  motion;  if  he  be  moved  towards  his  left 
hand,  the  current  will  be  against  him. 

227.  Faraday's  Disk  Machine.  —  Faraday  constructed 
several  magneto-electric  machines,  one  of  them  consist- 
ing of  a  copper  disk  (Fig.  132)  which  he  rotated  between 
the  poles  of  a  steel  magnet.     The  current  flowed  from 
shaft   to   rim  or   vice   versa,  according   to   the   sense   of 
the  rotation.     It  was  conducted  away  by  wires   having 
sliding   contacts.     In  other  machines   copper  wire   coils 


Fig.  131. 


CHAP.    Ill 


F  ATI  AD  AY'S  APPARATUS 


217 


.  132. 


were  spun  so  as  to  cut  magnetic  lines.  The  same  in- 
duction principle  is  applied  in  modern  dynamo-electric 
machines  (Lesson 
XLIL).  In  all  cases 
power  must  be  em- 
ployed to  produce 
the  motion.  They 
are  all  contrivances 
for  converting  me- 
chanical energy  into 
electrical  energy. 

228.  Faraday's 
Ring:  Principle 
of  Transformation.  — 
Amongst  Faraday's 
earliest  experiments  he  took  an  iron  ring  about  8  inches 
in  diameter  (Fig.  loo)  and  wound  upon  it  two  insulated 
coils  of  wire  P  and  S,  each  of  many  turns.  If  coil  P 
was  connected  to  a  battery  circuit,  and  coil  S  to  a 
galvanometer,  he  found  that  whenever  a  current  was 

turned  on  or  off  in  coil 
P,  secondary  currents 
were  generated  in  coil  S. 
In  fact  the  currents  in 
P  magnetized  the  iron 
ring,  and  the  magnetic 
lines  created  by  P  passed 
through  S,  setting  up 
induction  currents.  If 
S  is  used  as  the  primary 

then  P  will  work  as  secondary;  in  fact  the  induction  be- 
tween P  and  S  is  mutual.  The  Faraday  ring,  with  its  two 
coils  wound  upon  a  closed  circuit  of  iron,  maybe  regarded 
as  the  very  type  of  all  transformers  or  induction  coils. 
Faraday  also  employed  some  induction-coils  in  which 
the  two  coils  A  and  B  (Fig.  134)  were  wound  cylindri- 
cally  outside  one  another  upon  a  straight  core  C  of  iron. 


218  ELECTRICITY   AND   MAGNETISM        PART  i 

In  all  transformers  the  electromotive-forces  generated 
in  the  secondary  circuit  are   to  those  employed  in   the 
primary  circuit,  nearly  in  the  same 
proportion  as  the  relative  numbers  of 
turns  in  the  two  coils.     For  example, 
if  the  primary  coil  has  100  turns  and 
the  secondary  has   2500   turns,  the 
electromotive-force  in  the  secondary 
circuit    will    be    nearly    twenty-five 
times  as  great  as  that  used  in  the 
primary.      By   choosing   the  proper 
number  of  turns,  the  electromotive-force  can  be  trans- 
formed either  up  or  down. 

229.  The  Induction  Coil. —  In  order  to  generate 
enormously  high  electromotive-forces  which  shall  be  able 
to  send  sparks  across  air  spaces  that  ordinary  batteries 
working  at  under  100  volts  could  not  possibly  pierce, 
advantage  is  taken  of  the  transformer  principle.  To  pro- 
duce spark  discharges  there  is  used  the  apparatus  depicted 
in  Fig.  135,  as  improved  by  Callan,  Sturgeon,  Ruhmkorff, 
and  others,  and  termed  the  Induction  Coil  or  Inductorium. 
The  induction  coil  consists  of  a  cylindrical  bobbin  hav- 
ing a  central  iron  core  surrounded  by  a  short  inner  or 
"  primary  "  coil  of  stout  wire,  and  by  an  outer  "  second- 
ary "  coil  consisting  of  many  thousand  turns  of  very  fine 
wire,  very  carefully  insulated  between  its  different  parts. 
The  primary  circuit  is  joined  to  the  terminals  of  a  few 
powerful  Grove's  or  Bunsen's  cells,  and  in  it  are  also 
included  an  interrupter  and  a  commutator  or  key.  The 
object  of  the  interrupter,  is  to  make  and  break  the 
primary  circuit  in  rapid  succession.  The  result  of  this 
is  at  every  "  make  "  to  induce  in  the  outer  "  secondary  " 
circuit  a  momentary  inverse  current,  and  at  every 
"break"  a  powerful  momentary  direct  current.  As 
the  number  of  magnetic  lines  created  and  destroyed  at 
each  "  make  "  and  "  break  "  is  the  same,  the  two  electro- 
motive impulses  are  equal ;  but  by  the  use  of  a  condenser 


CHAP,  in  INDUCTION   COIL  219 

the  current  at  "  make  "  is  caused  to  take  a  considerable 
fraction  of  time  to  grow,  whilst  at  "  break  "  the  cessation 
is  instantaneous.  The  rate  of  cutting  of  the  magnetic 
lines  is  therefore  much  greater  at  "  break "  than  at 
"  make."  The  induced  electromotive-forces  at  "  make  " 
last  longer,  but  are  feebler,  and  do  not  suffice  to  send 
sparks.  The  currents  at  "  break "  manifest  themselves 
as  a  brilliant  torrent  of  sparks  between  the  ends  of  the 


Fig.  135. 

secondary  wires  when  brought  near  enough  together. 
The  primary  coil  is  made  of  stout  wire,  that  it  may 
carry  strong  magnetizing  currents,  and  consists  of  few 
turns  to  keep  the  resistance  low,  and  to  avoid  self-induc- 
tion of  the  primary  current  on  itself.  The  central  iron 
core  is  for  the  purpose  of  increasing,  by  its  great  mag- 
netic permeability,  the  number  of  lines  of  force  that  pass 
through  the  coils :  it  is  usually  made  of  a  bundle  of  fine 
wires  to  avoid  the  induced  currents  which  if  it  were  a 
solid  bar  would  be  set  circulating  in  it,  and  which  would 
retard  its  rapidity  of  magnetization  or  demagnetization. 


220  ELECTRICITY   AND   MAGNETISM        PART  i 

The  secondary  coil  is  made  with  many  turns,  in  order 
that  the  coefficient  of  transformation  may  be  large;  and 
as  the  induced  electromotive-force  will  be  thousands  of 
volts,  the  resistance  of  this  coil  will  be  immaterial,  and  it 
may  be  made  of  the  thinnest  wire  that  can  conveniently 
be  wound.  In  Mr.  Spottiswoode's  giant  Induction  Coil 
(which  yields  a  spark  of  42 £  inches'  length  in  air,  when 
worked  with  30  Grove's  cells),  the  secondary  coil  contains 
280  miles  of  wire,  wound  in  340,000  turns,  and  has  a 
resistance  of  over  100,000  ohms. 

The  interrupters  of  induction  coils  are  usually  self- 
acting.  That  of  Foucault,  shown  with  the  coil  in  Fig. 
135,  consists  of  an  arm  of  brass  L,  which  dips  a  platinum 
wire  into  a  cup  of  mercury  M,  from  which  it  draws  the 
point  out,  so  breaking  circuit,  in  consequence  of  its  other 
end  being  attracted  toward  the  core  of  the  coil  whenever  it 
is  magnetized;  the  arm  being  drawn  back  again  by  a  spring 
when,  on  the  breaking  of  the  circuit,  the  core  ceases  to  be 
a  magnet.  A  more  common  interrupter  on  small  coils  is 
a  "  break,"  consisting  of  a  piece  of  thin  steel  which  makes 
contact  with  a  platinum  point,  and  which  is  drawn  back  by 
the  attraction  of  the  core  on  the  passing  of  a  current ;  and 
so  makes  and  breaks  circuit  by  vibrating  backwards  and 
forwards  just  as  does  the  hammer  of  an  ordinary  electric 
bell. 

Associated  with  the  primary  circuit  of  a  coil  is  usually 
a  small  condenser  (see  Art.  303),  made  of  alternate  layers 
of  tinfoil  arid  paraffined  paper,  into  which  the  current 
flows  whenever  circuit  is  broken.  The  effect  of  the  con- 
denser is,  as  stated  above,  to  suppress  the  "  inverse  " 
current  at  "  make  "  and  to  increase  greatly  the  direct 
electromotive-force  at  "  break."  The  sparks  are  longer, 
and  only  pass  one  way.  The  condenser  does  this  by  the 
action  known  as  electric  resonance  (see  Art.  517). 

230.  Ruhmkorff 's  Reverser.  —  In  order  to  cut  off  or 
reverse  the  direction  of  the  battery  current  at  will, 
Ruhmkorff  applied  the  current-reverser,  or  reversing- 


CHAP.    Ill 


INDUCTION  SPARKS 


221 


switch  ("commutator")  shown  in  Fig.  136.  In  this 
instrument  the  battery  poles  are  connected  through  the 
ends  of  the  axis  of  a  small  ivory  or  ebonite  cylinder  to 
two  cheeks  of  brass  V  and  V,  which  can  be  turned  so  as 
to  place  them  either  way  in  contact  with  two  vertical 
springs  B  and  C,  which  are  joined  to  the  ends  of  the 
primary  coil.  Many  other  forms  of  reversing-switch 
have  been  devised ;  one,  much  used  as  a  key  for  tele- 
graphic signalling,  is  drawn  in  Fig.  271. 


231.  Luminous  Effects  of  Induction  Sparks.  —  The 
induction  coil  furnishes  a  rapid  succession  of  sparks 
with  which  all  the  effects  of  disruptive  discharge  may 
be  studied.  These  sparks  differ  only  in  degree  from 
those  furnished  by  friction  machines  and  by  Leyden 
jars  (see  Lesson  XXIV.  on  Phenomena  of  Discharge). 

For  studying  discharge  through  glass  vessels  and  tubes 
from  which  the  air  has  been  partially  exhausted,  the  coil 
is  very  useful.  Fig.  137  illustrates  one  of  the  many 
beautiful  effects  which  can  be  obtained,  the  spark  ex- 
panding in  the  rarefied  gas  into  nickering  sheets  of 
light,  exhibiting  stria)  and  other  phenomena. 


222 


ELECTRICITY   AND   MAGNETISM        PART  i 


232.    Induction  Currents  from  Earth's  Magnetism.  — 

It  is  easy  to  obtain  induced  currents  from  the  earth's 

magnetism.  A  coil  of  fine 
wire  joined  to  a  sensitive 
galvanometer,  when  sud- 
denly inverted,  cuts  the 
lines  of  the  earth's  magne- 
tism, and  induces  a  current. 
Faraday,  indeed,  applied 
this  method  to  investigate 
the  direction  and  number  of 
magnetic  lines.  If  a  small 
wTire  coil  be  joined  in  circuit 
with  a  suitable  galvanometer 
having  a  heavy  needle,  and 
the  little  coil  be  suddenly 
inverted  while  in  a  magnetic 
field,  it  will  cut  twice  all  the 
lines  that  pass  through  its 
own  area,  and  the  sine  of 
half  the  angle  of  the  first 
swing  (Art.  418)  will  be  pro- 
portional to  the  number  of 
lines  cut ;  for  with  a  slow- 
moving  needle,  the  total 
quantity  of  electricity  that 
Hows  through  the  coils  will 
be  the  integral  whole  of  all 
the  separate  quantities  con- 
veyed by  the  induced  cur- 
Fig  137  rents,  strong  or  weak,  which 

flow  round  the  circuit  during 

the  rapid  process  of  cutting  the  lines.  The  little  exploring 
coil  acts  therefore  as  a  magnetic  proof-plane.  For  small 
deflexions  the  first  swing  may  be  taken  as  a  sufficient 
approximation  instead  of  the  sine  of  half  the  angle  (see 
Art.  418). 


CHAP,  in        CHEMICAL  DECOMPOSITION  223 

If  the  circuit  be  moved  parallel  to  itself  across  a  uni- 
form magnetic  field  there  will  be  no  induction  currents, 
for  just  as  many  magnetic  lines  will  be  cut  in  moving 
ahead  in  front  as  are  left  behind.  There  will  be  no  cur- 
rent in  a  wire  moved  parallel  to  itself  along  a  line  of 
force ;  nor,  if  it  lie  along  such  a  line  while  a  current  is 
sent  through  it,  will  it  experience  any  mechanical  force. 

233.  Earth  Currents.  —  The  variations  of  the  earth's 
magnetism,  mentioned  in  Lesson  XII.,  alter  the  number 
of  magnetic  lines  which  pass  through  the  telegraphic  cir- 
cuits, and  hence  induce  in  them  disturbances  which  are 
known   as   "  earth   currents."     During  magnetic  storms 
the  earth  currents  on  the  British  lines  of  telegraph  have 
been   known   to   attain   a  strength  of   40   milliamperes, 
which   is    stronger    than   the    usual    working    currents. 
Feeble  earth  currents  are  observed  every  day,  and   are 
more  or  less  periodic  in  character. 

LESSON  XIX.  —  Chemical  Actions  of  Currents 

234.  Conducting  Properties  of  Liquids.  —  In  addition 
to  the  chemical  actions  inside  the  cells  of  the  battery, 
which   always    accompany  the  production  of  a  current, 
there   are   also   chemical   actions   produced  outside   the 
battery  when  the  current  is  caused  to  pass  through  cer- 
tain liquids.     Liquids  may  be  divided  into  three  classes 
—  (1)  those  which  do  not  conduct  at  all,  such  as  turpentine 
and   many  oils,  particularly  petroleum;  (2)  those   which 
conduct  without  decomposition,  viz.  mercury  and  other  mol- 
ten metals,  which  conduct  just  as  solid  metals  do ;  (3) 
those   which  are  decomposed  wlien  they  conduct   a   current, 
viz.  the  dilute  acids,  solutions  of  metallic  salts,  and  cer- 
tain fused  solid  compounds. 

235.  Decomposition   of  Water.  —  In   the  year   1800 
Carlisle  and  Nicholson  discovered  that  the  voltaic  cur- 
rent could  be  passed  through  water,  and  that  in  passing 
through  it  decomposed  a  portion  of  the  liquid  into  its 


224  ELECTRICITY   AND   MAGNETISM       PART  i 

constituent  gases.  These  gases  appeared  in  bubbles  on 
the  ends  of  the  wires  which  led  the  current  into  and  out 
of  the  liquid;  bubbles  of  oxygen  gas  appearing  at  the 
point  where  the  current  entered  the  liquid,  and  hydrogen 
bubbles  where  it  left  the  liquid.  Tt  was  soon  found  that 
a  great  many  other  liquids,  particularly  dilute  acids  and 
solutions  of  metallic  salts,  could  be  similarly  decomposed 
by  passing  a  current  through  them. 

236.  Electrolysis.  —  To  this  process  of  decomposing 
a  liquid  by  means  of  an  electric  current  Faraday  gave 
the  name  of  electrolysis  (i.e.  electric  analysis)  ;  and  those 
substances  which  are  capable  of  being  thus  decomposed 
or  "  electrolysed  "  he  termed  electrolytes. 

The  ends  of  the  wires  leading  from  and  to  the  battery 
are  called  electrodes;  and  to  distinguish  them,  that  by 
which  the  current  enters  is  called  the  anode,  that  by 
which  it  leaves  the  kathode.  The  vessel  in  which  a 
liquid  is  placed  for  electrolysis  is  termed  an  electrolytic 
cell 

237.  Electrolysis  of  Water.  —  Returning  to  the  de- 
composition  of  water,   we   may   remark  that  perfectly 
pure  water  appears  not  to  conduct,  but  its  resistance  is 
greatly  reduced  by  the  addition  of  a  few  drops  of  sul- 
phuric or  of  hydrochloric  acid.     The  apparatus  shown  in 
Fig.  138  is  suitable  for  this  purpose.     Here  a  battery  of 
two  cells  (those  shown  are  circular  Bunsen's  cells)  is  seen 
with  its  poles  connected  to  two  strips  of  metallic  platinum 
as  electrodes,  which  project  up  into  a  vessel  containing 
the   acidulated   water.      Two    tubes  closed   at  one  end, 
which   have   been  previously  rilled  with  water   and   in- 
verted, receive    the    gases    evolved    at    the    electrodes. 
Platinum  is  preferred  to  other  metals  such  as  copper  or 
iron  for  electrodes,  since  it  is  less  oxidizable  and  resists 
every  acid.     It  is  found  that  there  is  almost  exactly  twice 
as  much  hydrogen  gas  (by  volume)  evolved  at  the  kathode 
as  there  is  of  oxygen  at  the  anode.     This  fact  corresponds 
with  the  known  chemical  composition  of  water,  which  is 


CHAP,  in        ELECTROLYSIS  OF   WATER 


225 


produced  by  combining  together  these  two  gases  in  the 
proportion  of  two  volumes  of  the  former  to  one  of  the 
latter.  The  proportions  of  gases  evolved,  however,  are 
not  exactly  two  to  one,  for  at  first  a  very  small  quantity 
of  the  hydrogen  is  absorbed  or  "occluded"  by  the  plati- 
num surface,  while  a  more  considerable  proportion  of  the 
oxygen  —  about  1  per  cent  —  is  given  off  in  the  denser 


allotropic  form  of  ozone,  which  occupies  less  space  and 
is  also  slightly  soluble  in  the  water.  When  a  sufficient 
amount  of  the  gases  has  been  evolved  and  collected 
they  may  be  tested;  the  hydrogen  by  showing  that  it 
will  burn,  the  oxygen  by  its  causing  a  glowing  spark 
on  the  end  of  a  splinter  of  wood  to  burst  into  flame. 
If  the  two  gases  are  collected  together  in  a  common 
receiver,  the  mixed  gas  will  be  found  to  possess  the  well- 
known  explosive  property  of  mixed  hydrogen  and  oxygen 
gases.  The  chemical  decomposition  is  expressed  in  the 
following  equation : 


H20 

Water 


yields 
Q 


H2 

2  vols.  of  Hydrogen 


+ 
and 


o 

1  vol.  of  Oxygen. 


ELECTRICITY   AND   MAGNETISM        PART  i 


238.  Electrolysis  of  Sulphate  of  Copper.  —  We  will 
take  as  another  case  the  electrolysis  of  a  solution  of  the 
well-known  "  blue  vitriol "  or  sulphate  of  copper.     If  a 
few  crystals  of  this  substance  are  dissolved  in  water  a 
blue  liquid  is  obtained,  which  is  easily  electrolyzed  be- 
tween two  electrodes  of  platinum  foil,  by  the  current  from 
a  single  cell  of  any  ordinary  battery.     The  chemical  for- 
mula for  sulphate  of  copper  is  CuSO4.     The  result  of  the 
electrolysis  is   to  split  it  up  into  two  parts.      Metallic 
copper  is  carried  forward  by  the  current  and  deposited 
in  a  film  upon  the  kathode,  leaving  behind  at  the  anode 
"  sulphion,"  an  easily  decomposed  compound  of  sulphur 
and  oxygen,  which  is   immediately  acted   upon  by  the 
water  forming  sulphuric  acid  and  oxygen.     This  oxygen 
is  liberated  in   bubbles  at  the   anode.      The   chemical 
changes  are  thus  expressed : 

CuSO4  Cu          +         SO4 

Sulphate  of  Copper        becomes        Copper        and       Sulphion; 

SO4       +      H2O  H2SO4          +          O 

Sulphion      and      water        produce        Sulphuric  acid        and        Oxygen. 

In  this  way,  as  the  current  continues  to  flow,  copper 
is  continually  withdrawn  from  the  liquid  and  deposited 
on  the  kathode,  and  the  liquid  gets  more  and  more  acid. 
If  copper  electrodes  are  used,  instead  of  platinum,  no 
oxygen  is  given  off  at  the  anode,  but  the  copper  anode 
itself  dissolves  away  into  the  liquid  at  exactly  the  same 
rate  as  the  copper  of  the  liquid  is  deposited  on  the 
kathode. 

239.  Anions  and  Kations.  —  The  atoms  which  thus 
are  severed  from  one  another  and  carried   invisibly  by 
the  current  to  the  electrodes,  and  there   deposited,  are 
obviously  of  two  classes ;   some  are  left  behind   at  the 
anode,  others  are  carried  forward  to  the  kathode.     Fara- 
day gave  the  name   of  ions  to  these  wandering  atoms; 
those  left  at  the  anode  being  anions,  and  those  going 
to  the  kathode  being  kations.     Anions  are  sometimes 


CHAP,  in          LAWS   OF   ELECTROLYSIS  227 

regarded  as  "electronegative,"  because  they  move  as  if 
attracted  toward  the  4-  pole  of  the  battery,  while  the 
kations  are  regarded  as  "electropositive."  Hydrogen 
and  the  metals  are  kations,  moving  apparently  with  the 
direction  assumed  as  that  of  the  current,  and  are  de- 
posited where  the  current  leaves  the  electrolytic  cell. 
The  anions  are  oxygen,  chlorine,  etc.  When,  for  ex- 
ample, chloride  of  tin  is  electrolyzed,  metallic  tin  is 
deposited  on  the  kathode,  and  chlorine  gas  is  evolved  at 
the  anode. 

24O.   Quantitative  Laws  of  Electrolysis. 

(i.)  The  amount  of  chemical  action  is  equal  at  all  points 
of  a  circuit.  If  two  or  more  electrolytic  cells  are  placed 
at  different  points  of  a  simple  circuit  the  amount  of 
chemical  action  will  be  the  same  in  all,  for  the  same 
quantity  of  electricity  flows  past  every  point  of  the  cir- 
cuit in  the  same  time.  If  all  these  cells  contain  acidu- 
lated water,  the  quantity,  for  example,  of  hydrogen  set 
free  in  each  will  be  the  same ;  or,  if  they  contain  a  solu- 
tion of  sulphate  of  copper,  identical  quantities  of  copper 
will  be  deposited  in  each.  If  some  of  the  cells  contain 
acidulated  water,  and  others  contain  sulphate  of  copper, 
the  weights  of  hydrogen  and  of  copper  will  not  be  equal, 
but  will  be  in  chemically  equivalent  quantities. 

(ii.)  The  amount  of  an  ion  liberated  at  an  electrode  in 
a  given  time  is  proportional  to  the  strength  of  the  current. 
A  current  of  two  amperes  will  cause  just  twice  the  quan- 
tity of  chemical  decomposition  to  take  place  as  a  current 
of  one  ampere  would  do  in  the  same  time. 

(iii.)  The  amount  of  an  ion  liberated  at  an  electrode  in 
one  second  is  equal  to  the  strength  of  the  current  multiplied 
by  the  "  electro-chemical  equivalent "  of  the  ion.  It  has  been 
found  by  experiment  that  the  passage  of  one  coulomb  of 
electricity  through  water  liberates  -000010384  gramme 
of  hydrogen.  Hence,  a  current  the  strength  of  which 
is  C  (amperes}  will  liberate  C  x  -000010384  grammes 
of  hydrogen  per  second.  The  quantity  -000010384  is 


228 


ELECTRICITY   AND   MAGNETISM        PART 


called  the  electrochemical  equivalent  of  hydrogen.  The 
"  electrochemical  equivalents  "  of  other  elements  can  be 
easily  calculated  if  their  chemical  "equivalent "  is  known. 
Thus  the  chemical  "equivalent"*  of  copper  is  31-59; 
multiplying  this  by  '000010384  we  get  as  the  electro- 
chemical equivalent  of  copper  the  value  -0003281 
(gramme). 


TABLE  OF  ELECTROCHEMICAL  EQUIVALENTS,  ETC. 


Element. 

Atomic 
Weight. 

Val- 
ency. 

Chemical 
Equiva- 
lent. 

Electrochemical 
Equivalent 
(grammes 
JUT  coulomb). 

Electropositive  — 

Hydrogen    . 

1 

1 

1 

0-000010384 

Potassium   . 

39-03 

1 

39-03 

0-0004053 

Sodium 

23- 

1 

23- 

0-0002388 

Gold     .... 

196-2 

3 

65-4 

0-0006791 

Silver   .... 

107-67 

1 

107-67 

0-0011181 

Copper  (Cupric)  . 

63-18 

2 

31-59 

0-0003281 

"      (Cuprous) 

63-18 

1 

63-18 

0-0006562 

Mercury  (Mercuric)    . 

199-8 

2 

99-9 

0-0010374 

"        (Mercurous) 

199-8 

1 

199-8 

0-0020748 

Tin  (Stannic)       . 

117-8 

4 

29-45 

0-0003058 

"  (Stannous)    . 

117-8 

2 

58-9 

0-0006116 

Iron  (Ferrous)     . 

55-9 

2 

27-95 

0-0002902 

"     (Ferric) 

55-9 

(*) 

18-64 

0-0001935 

Nickel. 

58-6 

2 

29-3 

0-0003043 

Zinc     .... 

64-9 

2 

32-45 

0-00033698 

Lead    .... 

206-4 

2 

103-2 

0-0010716 

Electronegative  — 

Oxygen 

15-96 

2 

7-98 

0-00008286 

Chlorine       . 

35-37 

1 

35-37 

0-0003673 

Iodine  .... 

126-54 

1 

126-54 

0-0013140 

Bromine 

79-76 

1 

79-76 

0-0008282 

Nitrogen 

14-01 

3 

4-67 

0-00004849 

*  The  chemical  equivalent  must  not  be  confounded  with  the  atomic 
weight.  The  atomic  weight  of  copper  is  63,  that  is  to  say,  its  atoms  are  63 
times  as  heavy  as  atoms  of  hydrogen.  But  in  chemical  combinations  one 


CHAP,  in  VOLTAMETER  229 

241.  Weight  of  Element  deposited.  —  The  following 
equation  embodies  the  rule  for  finding  the  weight  of  any 
given  ion  disengaged  from  an  electrolytic  solution  during 
a  known  time  by  a  current  of  known  strength.     Let  C  be 
the  current  (reckoned  in  amperes},  t  the  time  (in  seconds), 
z  the  electrochemical  equivalent,  and  w  the  weight  (in 
grammes)  of  the  element  liberated  ;  then 

w  -  zCt, 

or,  in  words,  the  weight  (in  grammes)  of  an  element  depos- 
ited by  electrolysis  is  found  by  multiplying  its  electrochemical 
equivalent  by  the  strength  of  the  current  (in  amperes),  and 
by  the  time  (in  seconds),  during  which  the  current  continues 
to  flow. 

Example.  —  A  current  from  five  Daniell's  cells  was  passed 
through  two  electrolytic  cells,  one  containing  a  solution 
of  silver,  the  other  acidulated  water,  for  ten  minutes. 
A  tangent  galvanometer  in  the  circuit  showed  the 
strength  of  the  current  to  be  '5  amperes.  The  weight 
of  silver  deposited  will  be  O'OOlllS  X  -5  x  10  x  60 
=  0'3354  gramme.  The  weight  of  hydrogen  evolved 
in  the  second  cell  will  be  '000010384  X  '5  X  10  X  60 
=  0-003115  gramme. 

242.  Voltameters.  —  The  second  of  the  above  laws, 
that  the  amount  of  an  ion  liberated  in  a  given  time  is 
proportional  to  the  current,  is  sometimes  known  as  Fara- 
day's Law,  from  its  discoverer.    Faraday  pointed  out  that 
it  affords  a  chemical  means  of  measuring  currents.     He 
gave  the  name  of  voltameter  to  an  electrolytic  cell  arranged 
for  the  purpose  of  measuring  the  current  by  the  amount 
of  chemical  action  it  effects. 

243.  Water-Voltameter.  —  The  apparatus  shown  in 
Fig.  138  might  be   appropriately  termed  a  Water-  Vol- 

atom  of  copper  replaces,  or  is  "  worth,"  two  atoms  of  hydrogen  ;  hence  the 
weight  of  copper  equivalent  to  1  of  hydrogen  is  %*  =  31£.  In  all  cases  the 


chemical  "equivalent"  is  the  quotient  .    The  above  table 

gives  full  statistical  information. 


230  ELECTRICITY   AND   MAGNETISM        PART  i 

tameter,  provided  the  tubes  to  collect  the  gases  be  grad- 
uated, so  as  to  measure  the  quantities  evolved.  The 
weight  of  each  measured  cubic  centimetre  of  hydrogen 
(at  the  standard  temperature  of  0°  C.,  and  pressure  of 
760  millims.)  is  known  to  be  -00008988  grammes.  Hence, 
if  the  number  of  cubic  centimetres  liberated  during  a 
given  time  by  a  current  of  unknown  strength  be  ascer- 
tained, the  mean  strength  of  the  current  can  be  calculated 
by  first  reducing  the  volume  to  weight,  and  then  divid- 
ing by  the  electrochemical  equivalent,  and  by  the  time. 
Each  coulomb  of  electricity  liberates  in  its  flow  -1155 
cubic  centimetres  of  hydrogen,  and  -0577  c.c.  of  oxygen. 
If  these  gases  are  collected  together  in  a  mixed-gas  volta- 
meter there  will  be  -1732  c.c.  of  the  mixed  gases  evolved 
for  every  coulomb  of  electricity  which  passes.  To  decom- 
pose 9  grammes  of  water,  liberating  1  gramme  of  H  and 
8  grammes  of  O,  requires  96,302  coulombs  to  be  sent 
through  the  liquid  with  an  electromotive-force  of  at  least 
1-47  volts  (see  Art.  487). 

244.  Copper  and  Silver  Voltameters.  —  As  mentioned 
above,  if  sulphate  of  copper  is  electrolyzed  between  two 
electrodes  of  copper,  the  anode  is  slowly  dissolved,  and 
the  kathode  receives  an  equal  quantity  of  copper  as  a 
deposit  on  its  surface.  One  coulomb  of  electricity  will 
cause  -0003281  gramme  to  be  deposited ;  and  to  deposit 
one  gramme  weight  requires  a  total  quantity  of  3048 
coulombs  to  flow  through  the  electrodes.  A  current  of 
one  ampere  deposits  in  one  hour  1-177  grammes  of  copper, 
or  4-0248  grammes  of  silver. 

By  weighing  one  of  the  electrodes  before  and  after 
the  passage  of  a  current,  the  gain  (or  loss)  will  be  pro- 
portional to  the  quantity  of  electricity  that  has  passed. 
In  1879  Edison,  the  inventor,  applied  this  method  for 
measuring  the  quantity  of  electricity  supplied  to  houses 
for  electric  lights  in  them ;  a  small  copper  voltameter 
being  placed  in  a  branch  of  the  circuit  which  supplied 
the  house,  to  serve  as  a  meter.  Various  other  kinds  of 


CHAP,  in     COMPARISON   OF   INSTRUMENTS 


231 


Fig.  139. 


supply  meters  have  been  proposed,  having  clockwork 
counters,  rolling  integrating  disks,  and  other  mechanical 
devices  to  add  up  the  total  quantity  of  electricity  con- 
veyed by  the  current  (see  Art.  442). 

245.  Comparison  of  Voltameters  with  Galvanometers. 
—  It  will  be  seen  that  both  Galvanometers  and  Voltameters 
are  intended  to  measure  the  strength  of  currents,  one 
by  magnetic,  the  other  by  chemical  means.  Faraday 
demonstrated  that  the  magnetic  and  the  chemical  actions 
of  a  current  are  propor- 
tional to  one  another.  In 
Fig.  139  is  shown  a  circuit 
that  is  branched  so  that 
the  current  divides,  part 
going  through  a  branch 
of  small  resistance  r  and 
part  through  a  branch  of 
larger  resistance  R.  The 
current  will  divide,  the 
greater  part  going  by  the 
path  of  lesser  resistance. 
Three  amperemeters  are 
used.  It  will  be  found 
that  the  number  of  amperes 
in  the  main  circuit  is  equal  to  the  sum  of  the  amperes 
in  the  two  branches.  In  Fig.  140  the  three  ampere- 
meters have  been  replaced  by  three  copper  voltameters. 
The  weight  of  copper  deposited  in  the  voltameter  A  in 
the  main  circuit  will  be  found  to  be  equal  to  the  sum  of 
the  weights  deposited  in  B  and  C  in  the  two  branches. 
A  galvanometer  shows,  however,  the  strength  of  the  cur- 
rent at  any  moment,  and  its  variations  in  strength  from 
one  moment  to  another,  by  the  position  of  the  needle. 
In  a  voltameter,  a  varying  current  may  liberate  the 
atoms  of  copper  or  the  bubbles  of  gas  rapidly  at  one 
moment,  and  slowly  the  next,  but  all  the  varying  quan- 
tities will  be  simply  added  together  in  the  total  yield. 


232  ELECTRICITY   AND   MAGNETISM        PAUT  i 

In  fact,  the  voltameter  gives  us  the  "  time  integral "  of 
the  current.  It  tells  us  what  quantity  of  electricity  has 
flowed  through  it  during  the  experiment,  rather  than 
how  strong  the  current  was  at  any  one  moment. 

246.  Chemical  Test  for  Weak  Currents. — A  very 
feeble  current  suffices  to  produce  a  perceptible  amount 
of  change  in  certain  chemical  substances.     If  a  few  crys- 
tals of  the  white  salt  iodide  of  potassium  are  dissolved  in 
water,  and  then  a  little  starch  paste  is  added,  a  very  sen- 
sitive electrolyte  is  obtained,  which  turns  to  a  dark  blue 
colour  at  the  anode  when  a  very  weak  current  passes 
through   it.     The   decomposition   of    the  salt  liberates 
iodine  at  the  anode,  which,  acting  on  the  starch,  forms  a 
coloured  compound.     White  blotting-paper,  dipped  into 
the  prepared  liquid,  and  then  laid  on  the  kathode  and 
touched  by  the  anode,  affords  a  convenient  way  of  exam- 
ining the  discoloration  due  to  a  current.     A  solution  of 
ferrocyanide  of  potassium  affords  when  using  an  anode 
of  iron  the  well-known  tint  of   Prussian  blue.     Bain 
proposed  to   utilize  this  in  a  Chemical  Writing  Tele- 
graph,   the  short  and  long  currents  transmitted  along 
the  line  being  thus  recorded  in  blue  marks  on  a  strip  of 
prepared  paper,  drawn   along  by  clockwork  under   an 
iron  stylus  joined  to  the  positive  wire.     Faraday  showed 
that  chemical  discoloration   of    paper   moistened  with 
starch   and  iodide  of  potassium  was  produced  by  the 
passage  of  electricity  from  sources  of  all  different  kinds 
—  frictional,  voltaic,  thermo-electric,  and  magneto-elec- 
tric,—  even  by  that  evolved  by  the  Torpedo   and  the 
Gymnotus.     In  fact,  he  relied  on  this  chemical  test  as 
one  proof  of  the  identity  of  the  different  kinds. 

247.  Internal  and  External  Actions.  —  In  an  earlier 
lesson  it  was  shown  that  the  quantity  of  chemical  action 
inside  the  cells  of   the  battery  was  proportional  to  the 
current.     Hence,  Law  (i.)  of   Art.  240  applies  both  to 
the  portion  of  the  circuit  within  the  battery  and  to  that 
without  it. 


REVERSIBILITY   OF   CELLS 


233 


Suppose  3  Daniell's  cells  are  being  employed  to  decompose 
water  in  a  voltameter.  Then  while  1  gramme  weight  (11,126 
cub.  centims.)  of  hydrogen  and  8  grammes  (5563  c.c.)  of  oxygen 
are  set  free  in  the  voltameter,  31-5  grammes  of  copper  will  be 
deposited  in  each  cell  of  the  battery,  and  (neglecting  loss  by  local 
action) ,  32'5  grammes  of  zinc  will  be  dissolved  in  each  cell. 

248.  Reversibility.  —  It  will  therefore  be  evident 
that  the  electrolytic  cell  is  the  converse  of  the  voltaic  cell. 
The  chemical  work  done  in  the  voltaic  cell  furnishes  the 
energy  of  the  current  which  that  cell  sets  up  in  the 
circuit.  In  the  electrolytic  cell  chemical  work  is  per- 
formed, the  necessary  energy  being  furnished  by  the  cur- 
rent of  electricity  which  is 
sent  into  the  cell  from  an 
independent  battery  or 
other  source.  It  is  im- 
portant to  note  the  bearing 
of  this  with  respect  to  the 
energy  of  the  circuit.  Sup- 
pose a  current  of  strength 
C  to  flow  through  a  cell  of 
which  the  electromotive- 
force  is  E,  and  which  acts 
in  the  same  direction  as  Fig.  ui. 

the  current.     The  energy 

given  to  the  circuit  per  second  by  this  cell  will  be  (Art. 
435)  the  product  of  C  and  E ;  the  chemical  energy  of 
the  voltaic  cell  entering  the  circuit  at  the  place  where 
the  chemical  action  is  going  on.  In  Fig.  141  the  current 
is  indicated  by  the  arrows  with  thick  shafts,  the  electro- 
motive-force by  the  feathered  arrow.  For  example,  if 
10  amperes  flow  through  a  Daniell  cell  acting  with  1-1 
volts  of  electromotive-force,  the  power  given  out  by  the 
cell  is  11  ivatts  (Art.  435).  But  if  the  cell  be  so  con- 
nected into  the  circuit,  as  in  Case  II.  of  Fig.  141,  that 
the  E.M.F.  of  the  cell  opposes  the  current  that  is  being 
driven  along  the  circuit,  then  the  energy  per  second 


EMF  helps  current. 
Energy  enters  circuit. 


EMF  opposes  current. 
Energy  leaves  circuit. 


234  ELECTRICITY   AND   MAGNETISM       PART  i 

will  be  the  product  of  C  and  —  E,  or  —  CE,  the  negative 
sign  indicating  that  the  circuit  is  losing  energy,  part  of 
its  energy  being  absorbed  in  the  cell  in  doing  chemical 
work.  If  current  is  sent  backwards  through  a  Daniell 
cell  the  chemical  processes  are  reversed,  copper  is  dissolved 
and  zinc  is  deposited.  But  all  cells  are  not  reversible  in 
their  chemical  action. 

A  theory  of  electrolysis,  and  some  examples  of  its 
application,  are  given  in  Art.  488  on  Electro-chemistry. 


LESSON  XX.  —  Physical  and  Physiological  Effects  of  the 
Current 

249.  Molecular  Actions.  —  Metal  conductors,  when 
subjected  to  the  prolonged  action,  of  currents,  undergo 
slow   molecular   changes.      Wires  of    copper   and   brass 
gradually   become   brittle   under   its   influence.     During 
the  passage  of  the  current  through  metallic  wires  their 
cohesion  is  temporarily  lessened,  and  there  also  appears 
to  be  a  decrease  in  their  coefficient  of  elasticity.     It  was 
thought  by  Edlund  that  a  definite  elongation  could  be 
observed  in  strained  wires  when  a  current  was  passed 
through  them;   but  it  has  not   yet   been   satisfactorily 
shown  that  this  elongation  is  independent  of  the  elonga- 
tion due  to  the  heating  of  the  wire  owing  to  the  resistance 
it  opposes  to  the  current. 

250.  Electric  Osmose.  —  Porret  observed  that  if  a 
strong  current  is  led  into  certain  liquids,  as  if  to  electro- 
lyze  them,  a  porous  partition  being  placed  between  the 
electrodes,  the  current  mechanically  carries  part  of  the 
liquid  through  the  porous  diaphragm,  so  that  the  liquid 
is  forced  up  to  a  higher  level  on  one  side  than  on  the 
other.     This  phenomenon,  known  as   electric  osmose,  is 
most  manifest  when  badly-conducting  liquids,  such   as 
alcohol  and  bisulphide  of  carbon,  are  used.     The  transfer 
through  the  diaphragm  takes  place  in  the  direction  of 


CHAP,  in    VARIOUS  EFFECTS  OF  CURRENTS        235 

the  current;    that  is  to  say,  the  liquid  is  higher  about 
the  kathode  than  round  the  anode. 

251.  Electric  Distillation.  —  Closely  connected  with 
the  preceding  phenomenon  is  that  of  the  electric  distilla- 
tion of  liquids.     It  was  noticed  by  Beccaria  that  an  elec- 
trified liquid  evaporated  more  rapidly  than  one  not  elec- 
trified.    Gernez  has  recently  shown  that  in  a  bent  closed 
tube,  containing  two  portions  of  liquid,  one  of  which  is 
made  highly  ~+  and  the  other  highly  — ,  the  liquid  passes 
over  from  +  to  — .     This  apparent  distillation  is  not  due 
to  difference  of  temperature,  nor  does  it  depend  on  the 
extent  of  surface  exposed,  but  is  effected  by  a  slow  creep- 
ing of  the  liquid  along  the  interior  surface  of  the  glass 
tubes.     Bad  conductors,  such  as  turpentine,  do  not  thus 
pass  over. 

252.  Diaphragm  Currents. — Professor  Qiiincke  dis- 
covered that  a  current  is  set  up  in  a  liquid  when  it  is 
forced  by  pressure  through  a  porous  diaphragm.     This 
phenomenon  may  be  regarded  as  the  converse  of  electric 
osmose.    The  E.M.F.  of  the  current  varies  with  the  press- 
ure and  with  the  nature  of  the  diaphragm.     When  water 
was  forced  at  a  pressure  of  one  atmosphere  through  sul- 
phur, the  difference  of  potential  was  over  9  volts.     With 
diaphragms  of  porcelain  and  bladder  the  differences  were 
only  '35  and  -01  volts  respectively. 

253.  Electro-Capillary  Phenomena.  —  If  a  horizontal 
glass  tube,  turned  up  at  the  ends,  be  filled  with  dilute 
acid,  and  a  single  drop  of  mercury  be  placed  at  about  the 
middle  of  the  tube,  the  passage  of  a  current  through  the 
tube  will  cause  the  drop  to  move  along  towards  the  nega- 
tive pole.     It  is  believed  that  the  liberation  of  very  small 
quantities  of  gas  by  electrolysis  at  the  surface  where  the 
mercury  and  acid  meet  alters  the  surface-tension  very 
considerably,  and  thus  a  movement  results  from  the  cap- 
illary forces.      Lippmann,  Dewar,  and  others  have  con- 
structed  upon   this   principle   capillary    electrometers,   in 
which  the  pressure  of  a  column  of  liquid  is  made  to  bal- 


230  ELECTRICITY  AND   MAGNETISM       PART  i 

ance  the  electro-capillary  force  exerted  at  the  surface  of 
contact  of  mercury  and  dilute  acid,  the  electro-capillary 
force  being  nearly  proportional  to  the  electromotive-force 
when  this  does  not  exceed  one  volt.  Fig.  142  shows  the 
capillary  electrometer  of  Dewar.  A  glass  tube  rests  hori- 
zontally between  two  glass  dishes  in  which  holes  have 


been  bored  to  receive  the  ends  of  the  tube.  It  is  filled 
with  mercury,  and  a  single  drop  of  dilute  acid  is  placed 
in  the  tube.  Platinum  wires  to  serve  as  electrodes  dip 
into  the  mercury  in  the  dishes.  An  E.M.F.  of  only  ^ 
volt  suffices  to  produce  a  measurable  displacement  of  the 
drop.  The  direction  of  the  displacement  varies  with 
that  of  the  current. 

254.  Physiological  Actions.  —  Currents  of  electricity 
passed  through  the  limbs  affect  the  nerves  with  certain 
painful  sensations,  and  cause  the  muscles  to  undergo 
involuntary  contractions.  The  sudden  rush  of  even  a 
small  charge  of  electricity  from  a  Ley  den  jar  charged  to 
a  high  potential,  or  from  an  induction  coil  (see  Fig.  135), 
gives  a  sharp  and  painful  shock  to  the  system.  The  cur- 
rent from  a  few  strong  Grove's  cells,  conveyed  through 
the  body  by  grasping  the  terminals  with  moistened 
hands,  gives  a  very  different  kind  of  sensation,  not  at 
all  agreeable,  of  a  prickling  in  the  joints  of  the  arms 
and  shoulders,  but  not  producing  any  spasmodic  con- 
tractions, except  it  be  in  nervous  or  weakly  persons, 
at  the  sudden  making  or  breaking  of  the  circuit.  The 
difference  between  the  two  cases  lies  in  the  fact  that 
the  tissues  of  the  body  offer  a  very  considerable  resist- 


CHAP,  in         PHYSIOLOGICAL   EFFECTS  237 

ance,  and  that  the  difference  of  potential  in  the  former 
case  may  be  many  thousands  of  volts ;  hence,  though 
the  actual  quantity  stored  up  in  the  Leyden  jar  is  very 
small,  its  very  high  E.M.F.  enables  it  at  once  to  over- 
come the  resistance.  The  battery,  although  it  might, 
when  working  through  a  good  conductor,  afford  in  one 
second  a  thousand  times  as  much  electricity,  cannot, 
when  working  through  the  high  resistance  of  the  body, 
transmit  more  than  a  small  fraction,  owing  to  its  limited 
E.M.F. 

After  the  discovery  of  the  shock  of  the  Leyden  jar  by 
Cunseus  in  1745  many  experiments  were  tried.  Louis 
XV.  of  France  caused  an  electric  shock  from  a  battery  of 
Leyden  jars  to  be  administered  to  700  Carthusian  monks 
joined  hand  in  hand,  with  prodigious  effect.  Franklin 
killed  a  turkey  by  a  shock  from  a  Leyden  jar. 

In  1752  Sulzer  remarked  that  "  if  you  join  two  pieces 
of  lead  and  silver,  and  then  lay  them  upon  the  tongue, 
you  will  notice  a  certain  taste  resembling  that  of  green 
vitriol,  while  each  piece  apart  produces  no  such  sensa- 
tion." This  galvanic  taste,  not  then  suspected  to  have 
any  connexion  with  electricity,  may  be  experienced  by 
placing  a  silver  coin  on  the  tongue  and  a  steel  pen  under 
it,  the  edges  of  them  being  then  brought  into  metallic 
contact.  The  same  taste  is  noticed  if  the  two  wires  from 
the  poles  of  a  single  voltaic  cell  are  placed  in  contact 
with  the  tongue. 

Hitter  discovered  that  a  feeble  current  transmitted 
through  the  eyeball  produces  the  sensation  as  of  a  bright 
flash  of  light  by  its  sudden  stimulation  of  the  optic  nerve. 
A  stronger  current  transmitted  by  means  of  moistened 
conductors  attached  to  the  battery  terminals  gave  a  sen- 
sation of  blue  and  green  colours  in  flowing  between  the 
forehead  and  the  hand.  Voii  Helmholtz,  repeating  this 
experiment,,  observed  only  a  wild  rush  of  colour.  Dr. 
Hunter  saw  flashes  of  light  when  a  piece  of  metal  placed 
under  the  tongue  was  touched  against  another  which 


238  ELECTRICITY   AND   MAGNETISM       PART  i 

touched  the  moist  tissues  of  the  eye.  Volta  and  Hitter 
heard  musical  sounds  when  a  current  was  passed  through 
the  ears ;  and  Humboldt  found  a  sensation  to  be  produced 
in  the  organs  of  smell  when  a  current  was  passed  from  the 
nostril  to  the  soft  palate.  Each  of  the  specialized  senses 
can  be  stimulated  into  activity  by  the  current.  Man  pos- 
sesses no  specialized  sense  for  the  perception  of  electrical 
forces,  as  he  does  for  light  and  for  sound ;  but  there  is  no 
reason  for  denying  the  possibility  that  some  of  the  lower 
creatures  may  be  endowed  with  a  special  electrical  sense. 

The  following  experiment  shows  the  effect  of  feeble 
currents  on  cold-blooded  creatures.  If  a  copper  (or  silver) 
coin  be  laid  on  a  piece  of  sheet  zinc,  and  a  common  garden 
snail  be  set  to  crawl  over  the  zinc,  directly  it  comes  into 
contact  with  the  copper  it  will  suddenly  pull  in  its  horns, 
and  shrink  in  its  body.  If  it  is  set  to  crawl  over  two 
copper  wires,  which  are  then  placed  in  contact  with  a 
feeble  voltaic  cell,  it  immediately  announces  the  estab- 
lishment of  a  current  by  a  similar  contraction.* 

255.  Muscular  Contractions.  —  In  1678  Swammer- 
dam  showed  to  the  Grand  Duke  of  Tuscany  that  when 
a  portion  of  muscle  of  a  frog's  leg  hanging  by  a  thread 
of  nerve  bound  with  silver  wire  was  held  over  a  copper 
support,  so  that  both  nerve  and  wire  touched  the  copper, 
the  muscle  immediately  contracted.  More  than  a  century 
later  Galvani's  attention  was  drawn  to  the  subject  by 
his  observation  of  spasmodic  contractions  in  the  legs  of 
freshly-killed  frogs  under  the  influence  of  the  "  return- 
shock"  experienced  every  time  a  neighbouring  electric 
machine  was  discharged.  Unaware  of  Swammerdam's 
experiment,  he  discovered  in  1786  the  fact  (alluded  to  in 
Art.  163  as  leading  ultimately  to  the  discovery  of  the 
Voltaic  Pile)  that  when  nerve  and  muscle  touch  two 
dissimilar  metals  in  contact  with  one  another  a  contrac- 
tion of  the  muscle  takes  place.  The  limbs  ,of  the  frog, 

*  It  will  scarcely  be'credited  that  a  certain  Jules  Alix  once  seriously  pro- 
posed a  system  of  telegraphy  based  on  this  physiological  phenomenon. 


CHAP.    Ill 


MUSCULAR   CONTRACTIONS 


239 


prepared  as  directed  by  Galvani,  are  shown  in  Fig.  143. 
After  the  animal  has  been  killed  the  hind  limbs  are  de- 
tached and  skinned ;  the  crural  nerves  and  their  attach- 
ments to  the  lumbar  vertebrae  remaining.  For  some 
hours  after  death  the  limbs  retain  their  contractile  power. 
The  frog's  limbs  thus  prepared  form  an  excessively  deli- 
cate galvanoscope  :  with  them,  for  example,  the  excessively 


Fig.  148. 

delicate  induction-currents  of  the  telephone  (Lesson  LILT.) 
can  be  shown,  though  the  most  sensitive  galvanometers 
barely  detect  them.  Galvani  and  Aldini  proved  that 
other  creatures  undergo  like  effects.  With  a  pile  of  100 
pairs  Aldini  experimented  on  newly-killed  sheep,  oxen, 
and  rabbits,  and  found  them  to  suffer  spasmodic  muscular 
contractions.  Humboldt  proved  the  same  on  fishes ;  and 
Zanotti,  by  sending  a  current  through  a  newly-killed 
grasshopper,  caused  it  to  emit  its  familiar  chirp.  Aldini, 


240  ELECTRICITY   AND   MAGNETISM       PART  i 

and  later  Dr.  Ure  of  Glasgow,  experimented  on  the  bodies 
of  executed  criminals,  with  a  success  terrible  to  behold. 
The  facial  muscles  underwent  horrible  contortions,  and 
the  chest  heaved  with  the  contraction  of  the  diaphragm. 
The  small  muscles  attached  to  the  roots  of  the  hairs  of 
the  head  appear  to  be  markedly  sensitive  to  electrical 
conditions  from  the  readiness  with  which  electrification 
causes  the  hair  to  stand  on  end. 

The  resistance  of  the  human  body  to  the  flow  of  electric 
current  through  it  depends  mainly  on  the  dryness  of  the 
skin.  It  may  vary  from  10,000,  down  to  300  ohms  when 
the  skin  is  moist.  From  experiments  made  in  America 
in  connexion  with  the  execution  of  criminals,  it  was 
found  that  the  average  resistance  of  the  human  body  is 
2500  ohms,  and  that  3000  (alternating)  volts  applied 
between  the  head  and  spine  caused  instantaneous  death. 

A  current  of  as  much  as  20  milliamperes  produces 
terrible  muscular  contractions,  whilst  a  current  of  2 
amperes  traversing  a  vital  part  is  almost  certainly  fatal. 
The  effect  of  the  current  is  twofold ;  in  the  first  place  it 
acts  upon  the  nerves,  causing  spasms,  secondly  it  destroys 
the  tissue  either  by  burning  or  by  electrolysis,  the  blood 
becoming  coagulated.  To  restore  a  person  who  has  been 
rendered  insensible  by  an  electric  shock,  all  the  same 
restoratives  should  be  used  as  for  a  person  drowned. 

256.  Conditions  of  Muscular  Contraction.  —  To  pro- 
duce muscular  contraction  the  current  must  traverse  a 
portion  of  the  nerve  longitudinally.  In  a  freshly-prepared 
frog  the  current  causes  a  contraction  only  momentarily 
when  the  circuit  is  made  or  broken.  A  rapidly  interrupted 
current  will  induce  a  second  contraction  before  the  first 
has  had  time  to  pass  off,  and  the  muscle  may  exhibit  thus 
a  continuous  contraction  resembling  tetanus.  The  pre- 
pared frog  after  a  short  time  becomes  less  sensitive,  and 
a  "  direct "  current  (that  is  to  say,  one  passing  along  the 
nerve  in  the  direction  from  the  brain  to  the  muscle)  only 
produces  an  effect  when  circuit  is  made,  while  an  "in- 


CHAP,  in  ANIMAL   ELECTRICITY  241 

verse "  current  only  produces  an  effect  when  the  circuit 
is  broken.  Matteucci,  who  observed  this,  also  discovered 
by  experiments  on  living  animals  that  there  is  a  distinction 
between  the  conductivity  of  sensory  and  motor  nerves,  — 
a  "  direct "  current  affecting  the  motor  nerves  on  making 
the  circuit,  and  the  sensory  nerves  on  breaking  it ;  while 
an  "  inverse  "  current  produced  inverse  results.  Little  is, 
however,  yet  known  of  the  conditions  of  conductivity  of 
the  matter  of  the  nerves ;  they  conduct  better  than  mus- 
cular tissue,  cartilage,  or  bone ;  but  of  all  substances  in 
the  body  the  blood  conducts  best.  Powerful  currents 
doubtless  electrolyze  the  blood  to  some  extent,  coagulat- 
ing it  and  the  albumin  it  contains.  The  power  of  con- 
tracting under  the  influence  of  the  current  appears  to  be 
a  distinguishing  property  of  protoplasm  wherever  it  occurs. 
The  amoeba,  the  most  structureless  of  organisms,  suffers 
contractions.  Hitter  discovered  that  the  sensitive  plant 
shuts  up  when  electrified,  and  Burdon  Sanderson  has 
shown  that  this  property  extends  to  other  vegetables, 
being  exhibited  by  the  carnivorous  plant,  the  Dionsea  or 
Venus'  Fly  Trap. 

257.  Animal  Electricity. — Although,  in  his  later 
writings  at  least,  Galvani  admitted  that  the  electricity 
thus  operating  arose  from  the  metals  employed,  he  insisted 
on  the  existence  of  an  animal  electricity  resident  in  the 
muscular  and  nervous  structures.  He  showed  that  con- 
tractions could  be  produced  without  using  any  metals  at 
all  by  merely  touching  a  nerve  at  two  different  points 
along  its  length  with  a  morsel  of  muscle  cut  from  a  living 
frog;  and  that  a  conductor  of  one  metal  when  joining  a 
nerve  to  a  muscle  also  sufficed  to  cause  contraction  in  the 
latter.  Galvani  and  Aldini  regarded  these  facts  as  a 
disproof  of  Volta's  contact-theory.  Volta  regarded  them 
as  proving  that  the  contact  between  nerve  and  muscle 
itself  produced  (as  in  the  case  of  two  dissimilar  metals) 
opposite  electrical  conditions.  Nobili,  later,  showed  that 
when  the  nerve  and  the  muscle  of  the  frog  were  respec- 

B 


242  ELECTRICITY   AND   MAGNETISM        PART  i 

tively  connected  by  a  water-contact  with  the  terminals  of 
a  delicate  galvanometer,  a  current  is  produced  which  lasts 
several  hours :  he  even  arranged  a  number  of  frogs'  legs 
in  series,  like  the  cells  of  a  battery,  and  thus  increased  the 
current.  Matteucci  showed  that  through  the  muscle  alone 
there  may  be  an  electromotive-force.  Du  Bois  Reymond 
has  shown  that  if  the  end  of  a  muscle  be  cut  across,  the 
ends  of  the  muscular  fibres  of  the  transverse  section  are 
negative,  and  the  sides  of  the  muscular  fibres  are  positive, 
and  that  this  difference  of  potential  will  produce  a  current 
even  while  the  muscle  is  at  rest.  To  demonstrate  this  he 
employed  a  fine  astatic  galvanometer  with  20,000  turns 
of  wire  in  its  coils;  and  to  obviate  errors  arising  from  the 
contact  of  the  ends  of  the  wires  with  the  tissues  unpolariz- 
able  electrodes  were  used,  made  by  plunging  terminal  zinc 
points  into  a  saturated  solution  of  sulphate  of  zinc,  con- 
tained in  a  fine  glass  tube,  the  end  of  which  was  stopped 
with  a  porous  plug  of  moistened  china  clay.  Normal 
muscle  at  rest  shows  no  current  whatever  between  its 
parts.  Injured  muscle  at  rest  shows  a  current  from  the 
injured  toward  the  uninjured  part  (returning  toward  the 
injured  part  through  the  galvanometer).  Normal  muscle 
when  active  shows  a  current  from  the  active  part  toward 
the  resting  part.  Du  Bois  Reymond  obtained  currents 
from  his  own  muscles  by  dipping  the  tips  of  his  fore- 
fingers into  two  cups  of  salt  water  communicating  with 
the  galvanometer  terminals.  A  sudden  contraction  of 
the  muscles  of  either  arm  produced  a  current  from  the 
contracted  toward  the  uncontracted  muscles.  Dewar 
has  shown  that  when  light  falls  upon  the  retina  of  the 
eye  an  electric  current  is  set  up  in  the  optic  nerve. 
In  the  skin,  and  especially  in  the  skin  of  the  com- 
mon eel,  there  is  an  electromotive-force  from  without 
inwards. 

258.  Surgical  Applications.  —  Electric  currents  have 
been  successfully  employed  as  an  adjunct  in  restoring 
persons  rescued  from  drowning;  the  contraction  of  the 


CHAP,  in          SURGICAL    APPLICATIONS  243 

diaphragm  and  chest  muscles  serving  to  start  respiration. 
Since  the  discovery  of  the  Leyden  jar  many  attempts 
have  been  made  to  establish  an  electrical  medical  treat- 
ment. Discontinuous  currents,  particularly  those  fur- 
nished by  small  induction-coils  and  magneto-electric 
machines,  are  employed  by  practitioners  to  stimulate  the 
nerves  in  paralysis  and  other  affections.  Electric  cur- 
rents should  not  be  used  at  all  except  with  great  care, 
and  under  the  direction  of  regularly-trained  surgeons. 
It  is  not  out  of  place  to  enter  an  earnest  caution  on  this 
head  against  the  numerous  quack  doctors  who  deceive 
the  unwary  with  magnetic  and  galvanic  "appliances." 
In  many  cases  these  much-advertised  shams  have  done 
incalculable  harm:  in  the  very  few  cases  where  some 
fancied  good  has  accrued  the  curative  agent  is  probably 
not  magnetism,  but  flannel ! 

The  usual  pathological  dose  of  current  is  from  2  to  10 
milliamperes.  Apparatus  pretending  to  cure,  and  incapa- 
ble of  furnishing  such  currents,  is  worthless.  Continuous 
currents  appear  to  produce  a  sedative  effect  around  the 
anode,  which  is  of  service  in  neuralgia  and  painful  affec- 
tions, and  an  increase  in  irritability  around  the  kathode, 
useful  in  cases  of  paralysis.  The  continuous  current  is 
also  employed  electrolytically  to  disperse  tumours.  Al- 
ternate currents,  and  rapidly  interrupted  uni-directional 
currents  stimulate  the  nerves. 


Second 

CHAPTER  IV 

ELECTROSTATICS 

LESSON  XXI.  —  Theory  of  Potential 

259.  By  the  lessons  in  Chapter  I.  the  student  will 
have  obtained  some  elementary  notions  upon  the  exist- 
ence and  measurement  of  definite  quantities  of  electricity. 
In  the  present  lesson,  which  is  both  one  of  the  hardest 
and  one  of  the  most   important  to  the  beginner,  and 
which  he  must  therefore  study  the  more  carefully,  the 
laws  which  concern  the  magnitude  of  electrical  quantities 
and  their  measurement  are  more  fully  explained.     In  no 
branch  of  knowledge  is  it  more  true  than  in  electricity, 
that  "  science  is  measurement."    That  part  of  the  science 
of  electricity  which  deals  with  the  measurement  of  charges 
of  electricity  is  called  Electrostatics.     We  shall  begin  by 
discussing  first  the  simple  laws  of  electric  force,  which 
were  brought  to  light  in  Chapter  I.  by  simple  experi- 
mental means. 

260.  First  Law  of  Electrostatics.  —  Electric  charges 
of  similar  sign  repel  one  another,  but  electric  charges  of  op- 
posite signs  attract  one  another.     The   fundamental   facts 
expressed  in  this  Law  were  fully  explained  in  Lesson  I. 

244 


CHAP,  iv       LAW   OF  INVEESE   SQUARES  245 

Though  familiar  to  the  student,  and  apparently  simple, 
these  facts  require  for  their  complete  explanation  the  aid 
of  advanced  mathematical  analysis.  They  will  here  be 
treated  as  simple  facts  of  observation. 

261.  Second  Law  of  Electrostatics.  —  The  force 
exerted  between  two  charges  of  electricity  (supposing  them 
to  be  collected  at  points  or  on  two  small  spheres)  is  directly 
proportional  to  their  product,  and  inversely  proportional  to 
the  square  of  the  distance  between  them.  This  law,  discovered 
by  Coulomb,  and  called  Coulomb's  Law,  was  briefly  alluded 
to  (on  p.  21)  in  the  account  of  experiments  made  with 
the  torsion-balance;  and  examples  were  there  given  in 
illustration  of  both  parts  of  the  law.  We  saw,  too,  that 
a  similar  law  held  good  for  the  forces  exerted  between 
two  magnetic  point-poles.  Coulomb  applied  also  the 
method  of  oscillations  to  verify  the  indications  of  the 
torsion-balance  and  found  the  results  entirely  confirmed. 
We  may  express  the  two  clauses  of  Coulomb's  Law  in  the 
following  symbolic  manner.  Let  f  stand  for  the  force,  q 
for  the  quantity  of  electricity  in  one  of  the  two  charges, 
and  q'  for  that  of  the  other  charge,  and  let  r  stand  for 
the  distance  between  them.  Then, 

(1)  /is  proportional  to  q  x  q', 
and  (2)  /  is  proportional  to  —  . 

These  two  expressions  may  be  combined  into  one; 
and  it  is  most  convenient  so  to  choose  our  units  or 
standards  of  measurement  that  we  may  write  our  sym- 
bols as  an  equation  :  — 


262.  Unit  of  Electric  Quantity.  —  If  we  are,  how- 
ever, to  write  this  as  an  equality,  it  is  clear  that  we 
must  choose  our  unit  of  electricity  in  accordance  with 
the  units  already  fixed  for  measuring  force  and  distance. 


246  ELECTRICITY   AND   MAGNETISM     PART  n 

Electricians  of  all  nations  have  agreed  in  adopting  a 
system  which  is  based  upon  three  fundamental  units  : 
viz.  the  Centimetre  for  a  unit  of  length;  the  Gramme 
for  a  unit  of  mass  ;  the  Second  for  a  unit  of  time.  All 
other  units  can  be  derived  from  these,  as  is  explained 
in  the  note  at  the  end  of  this  lesson.  Now,  amongst 
the  derived  units  of  this  system  is  the  unit  of  force, 
named  the  Dyne,  which  is  that  force  which,  acting  for 
one  second  on  a  mass  of  one  gramme,  imparts  to  it 
a  velocity  of  one  centimetre  per  second.  Taking  the 
dyne  then  .as  the  unit  of  force,  and  the  centimetre  as  the 
unit  of  length  (or  distance),  we  must  find  a  unit  of  electric 
quantity  to  agree  with  these  in  our  equation.  It  is  quite 
clear  that  if  q,  q',  and  r  were  each  made  equal  to  1  (that 
is,  if  we  took  two  charges  of  value  1  each,  and  placed 

them  one  centimetre  apart),  the  value  of  ^ — j^-  would  be 

1x1 

r-  which   is   equal  to   1.     Hence  we  adopt,  as  our 

Definition  of  a  Unit  of  Electricity*  the  following,  which 
we  briefly  gave  at  the  end  of  Lesson  II.  One  Unit  of 
Electricity  is  that  quantity  which,  ivhen  placed  at  a  distance 
of  one  centimetre  (in  air)  from  a  similar  and  equal  quantity, 
repels  it  with  a  force  of  one  dyne. 

An  example  will  aid  the  student  to  understand  the 
application  of  Coulomb's  Law. 

Example.—  Two  small  spheres,  charged  respectively  with 
6  units  and  8  units  of  +  electricity,  are  placed  4  centi- 
metres apart  ;  find  what  force  they  exert  on  one 

another.      By    the    formula,  /  =  ^  ^  ,  we  find  /  = 

0X8      48 

_  =  -  =  3  dynes. 

The  force  in  the  above  example  would  clearly  be  a 
force   of   repulsion.      Had  one   of    these   charges  been 

*  That  is  one  unit,  in  the  electrostatic  system.   It  is  only  3555oW?H! of 
the  quantity  called  1  coulomb. 


CHAP,   iv  NOTIONS   OF   POTENTIAL  247 

negative,  the  product  q  x  q'  would  have  had  a  —  value, 
and  the  answer  would  have  come  out  as  minus  3  dynes. 
The  presence  of  the  negative  sign,  therefore,  prefixed  to 
a  force,  will  indicate  that  it  is  a  force  of  attraction,  whilst 
the  +  sign  would  signify  a  force  of  repulsion. 

The  intensity  of  an  electric  field  (Art.  266)  being 
measured  by  the  force  it  exerts  on  a  unit  charge,  it  at  once 
follows  that  at  a  distance  of  r  (in  air)  from  a  charge  q  the 
intensity  of  the  electric  field  due  to  that  charge  will  be 
fj/>''2.  If  the  intervening  medium  be  not  air,  but  have  a 
specific  dielectric  capacity  k,  the  field  will  be  only  q/kr^-. 

263.  Potential.  —  We  must  next  define  the  term 
potential,  as  applied  to  electric  forces ;  but  to  make  the 
meaning  plain  a  little  preliminary  explanation  is  necessary. 
Suppose  we  had  a  +  charge  on  a  small  insulated  sphere 
A  (see  Fig.  114),  placed  by  itself  far  from  all  other 
electric  charges  and  conductors.  If  we  were  to  bring 
another  positively-charged  body  B  near  it,  A  would  repel 
B.  But  the  repelling  force  would  depend  on  the  quantity 
of  the  new  charge,  and  on  the  distance  at  which  it  was 

P  Q  B"  B' 

/r\ /~\  /TV  .m_ 

\^7  \y  -^^7-       •  •-  "\^7    --' 

Fig.  144. 

placed.  Suppose  the  new  charge  thus  brought  near  to  be 
one  +  unit ;  when  B  was  a  long  way  off  it  would  be 
repelled  with  a  very  slight  force,  and  very  little  work 
need  be  expended  in  bringing  it  up  nearer  against  the 
repelling  forces  exerted  by  A ;  but  as  B  was  brought 
nearer  and  nearer  to  A,  the  repelling  force  would  grow 
greater  and  greater,  and  more  and  more  work  would  have 
to  be  done  against  these  opposing  forces  in  bringing  up 
B.  Suppose  that  we  had  begun  at  an  infinite  distance 
away,  and  that  we  pushed  up  our  little  test  charge  B  from 
B'  to  B"  and  then  to  Q,  and  so  finally  moved  it  up  to  the 
point  P,  against  the  opposing  forces  exerted  by  A,  we 


248  ELECTRICITY   AND   MAGNETISM      PART  n 

should  have  had  to  spend  a  certain  amount  of  work;  that 
work  represents  the  potential*  at  the  point  P  due  to  A. 
For  the  following  is  the  definition  of  electric  potential :  — 
The  potential  at  any  point  in  the  work  that  must  be  spent 
upon  a  unit  of  positive  electricity  in  bringing  it  up  to  that 
point  from  an  infinite  distance.  Had  the  charge  on  A  been 
a  —  charge,  the  force  would  have  been  one  of  attraction, 
in  which  case  we  should  have  theoretically  to  measure 
the  potential  at  P,  either  by  the  opposite  process  of  placing 
there  a  +  unit,  and  then  removing  it  to  an  infinite  dis- 
tance against  the  attractive  forces,  or  else  by  measuring 
the  amount  of  work  which  would  be  done  by  a  +  unit  in 
being  attracted  up  to  P  from  an  infinite  distance. 

It  can  be  shown  that  where  there  are  more  electrified 
bodies  than  one  to  be  considered,  the  potential  due  to 
them  at  any  point  is  the  sum  of  the  potentials  (at  that 
point)  of  each  one  taken  separately. 

It  can  also  be  shown  that  the  potential  at  a  point  P, 
near  an  electrified  particle  A,  is  equal  to  the  quantity  of 
electricity  at  A  divided  by  the  distance  between  A  and  P. 
Or,  if  the  quantity  be  called  q,  and  the  distance  r,  the 
potential  is  q  ->  r.  f 

Proof.  —  First  determine  the  difference  of  potential  between 
point  P  and  point  Q  due  to  a  charge  of  electricity  q  on  a  small 
sphere  at  A. 

Call  distance  AP  =  r,  and  AQ  =  r'.  Then  PQ  =  r'  —  r.  The 
difference  of  potential  between  Q  and  P  is  the  work  done  in 
moving  a  +  unit  from  Q  to  P  against  the  force ;  and  since 

*  In  its  widest  meaning  the  term  "  potential"  must  be  understood  as 
"power  to  do  work."  For  if  we  have  to  do  a  certain  quantity  of  work 
against  the  repelling  force  of  a  charge  in  bringing  up  a  unit  of  electricity 
from  an  infinite  distance,  just  so  much  work  has  the  charge  power  to  do, 
for  it  will  spend  an  exactly  equal  amount  of  work  in  pushing  the  unit  of 
electricity  back  to  an  infinite  distance.  If  we  lift  a  pound  five  feet  high 
against  the  force  of  gravity,  the  weight  of  the  pound  can  in  turn  do  five 
foot-pounds  of  work  in  falling  back  to  the  ground. 

t  The  complete  proof  would  require  an  elementary  application  of  the 
integral  calculus,  but  an  easy  geometrical  demonstration,  sufficient  for 
present  purposes,  is  given  below. 


CHAP,  iv  THEORY   OF  POTENTIAL  249 


work  =  (average)  force  X  distance  through  which  it  is 
overcome 


Force  at  P  exerted  by  q  on  a  +  unit  = 
and  the  force  at  Q  exerted  by  q  on  a  +  unit  =  q/r"2. 

Suppose  now  that  the  distance  PQ  be  divided  into  any  number 
(n)  of  equal  parts  rri,  r^,  r2rs,  .........  rn—ir'- 

The  force  at  r=q/r%. 

"    *\  =  q/r?  ....  etc. 

Now  since  r±  may  be  made  as  close  to  r  as  we  choose,  if  we 
only  take  n  a  large  enough  number,  we  shall  commit  no  serious 


1    I    I   I 

r    rt    ra  rs 


Fig.  145. 

error  in  supposing  that  r  X  r*±  is  a  fair  mean  between  r2  and  r-^ ; 
hence  we  may  assume  the  average  force  over  the  short  length 

q 
from  r  to  r:  to  be  — • 

Hence  the  work  done  in  passing  from  TI  to  r  will  be 


On  a  similar  assumption,  the  work  done  in  passing  from  r2  to 
TI,  will  be 

=  q  [  —  —  —  |  ,  and  that  done  from  r»  to  r2  will  be 
\fi     W 

=  q[  —  —  —  }  ,  etc.,  giving  us  n  equations,  of  which  the 

\r*    rz/ 
last  will  be  the  work  done  in  passing  from  r'  to  rn_1 


Adding  up  all  these  portions  of  the  work,  the  intermediate 


250  ELECTRICITY  AND   MAGNETISM      PART  n 


values  of  r  cancel  out,  and  we  get  for  the  work  done  in  passing 
from  Q  to  P 


Next  suppose  Q  to  be  an  infinite  distance  from  A.  Here 
r  =  infinity,  and  —  =  0.  In  that  case  the  equation  becomes 

VP  =  |. 

If  there  are  a  number  of  electrified  particles  at  different 
distances  from  P,  the  separate  values  of  the  potential  q/r 
due  to  each  electrified  particle  separately  can  be  found, 
and  therefore  the  potential  at  P  can  be  found  by  dividing  the 
quantity  of  each  charge  by  its  distance  from  the  point  P,  and 
then  adding  up  together  the  separate  amounts  so  obtained. 
The  symbol  V  is  generally  used  to  represent  potential. 
The  potential  at  P  we  will  call  VP,  then 


This  expression  "%q/r  represents  the  work  done  on  or  by 
a  unit  of  -f  electricity  when  moved  up  to  the  given  point 
P  from  an  infinite  distance,  according  as  the  potential  at 
P  is  positive  or  negative. 

264.  Zero  Potential.  —  At  a  place  infinitely  distant 
from  all  electrified  bodies  there  would  be  no  electric  forces 
and  the  potential  would  be  zero.     For  purposes  of  conven- 
ience it  is,  however,  usual  to  consider  the  potential  of  the 
earth  as  an  arbitrary  zero,  just  as  it  is  convenient  to  con- 
sider "  sea-level "  as  a  zero  from  which  to  measure  heights 
or  depths  (see  Art.  269). 

265.  Difference  of  Potentials.  —  Since  potential  repre- 
sents  the    work    that   must   be   done   on    a    -f    unit   in 
bringing  it  up  from  an  infinite  distance,  the  difference  of 


CHAP,  iv      DIFFERENCE    OF   POTENTIALS  251 

potential  between  two  points  is  the  work  to  be  done  on 
or  by  a  +  unit  of  electricity  in  carrying  it  from  one  point 
to  the  other.  Thus  if  Vp  represents  the  potential  at  P, 
and  YQ  the  potential  at  another  point  Q,  the  difference  of 
potentials  Vp  —  VQ  denotes  the  work  done  in  moving  up 
the  +  unit  from  Q  to  P.  It  is  to  be  noted  that  since  this 
value  depends  only  on  the  values  of  the  potential  at  P 
and  at  Q,  and  not  on  the  values  at  intermediate  points, 
the  work  done  will  be  the  same,  whatever  the  path  along 
which  the  particle  moves  from  Q  to  P.  In  the  same  way 
it  is  true  that  the  expenditure  of  energy  in  lifting  a 
pound  (against  the  earth's  attraction)  from  one  point  to 
another  on  a  higher  level,  will  be  the  same  whatever  the 
path  along  which  the  pound  is  lifted. 

266.  Electric  Force.  — The  definition  of  "work"  is 
the  product  of  the  force   overcome   into  the   distance 
through  which  the  force  is  overcome ;   or  work  =  force 

x  distance  through  which  it  is  overcome. 

Hence,  if  the  difference  of  potential  between  two  points 
is  the  work  done  in  moving  up  our  +  unit  from  one 
point  to  the  other,  it  follows  that  the  average  electric 
force  between  those  points  will  be  found  by  dividing  the 
work  so  done  by  the  distance  between  the  points ;  or 

PTO    Q  =  /  (the  average  electric  force  along  the  line 

PQ).  The  (average)  electric  force  is  therefore  the  rate 
of  change  of  potential  per  unit  of  length.  If  P  and  Q 
are  near  together  the  force  will  be  practically  uniform 
between  P  and  Q.  The  term  electromotive  intensity  is 
sometimes  used  for  the  force  in  an  electric  field. 

We  may  represent  this  intensity  of  the  electric  field 
by  supposing  the  number  of  electric  lines  per  square 
centimetre  to  be  drawn  to  represent  the  number  of  dynes 
of  force  on  a  +  unit  placed  at  the  point. 

267.  Equipotential    Surfaces.  —  A    charge    of    elec- 
tricity collected  on  a  small  sphere  acts  on  external  bodies 
as  if  the  charge  were  all  collected  into  one  point  at  its 


252 


ELECTRICITY  AND   MAGNETISM      PART  n 


centre.*  We  have  seen  that  the  force  exerted  by  such  a 
charge  falls  off  at  a  distance  from  the  ball,  the  force 
becoming  less  and  less  as  the  square  of  the  distance 
increases.  But  the  force  is  the  same  in  amount  at  all 
points  equally  distant  from  the  small  charged  sphere. 
And  the  potential  is  the  same  at  all  points  that  are 
equally  distant  from  the  charged  sphere.  If,  in  Fig.  145, 
the  point  A  represents  the  sphere  charged  with  q  units  of 


\ 


Fig.  146. 

electricity,  then  the  potential  at  P,  which  we  will  call 
VP,  will  be  equal  to  q/r,  where  r  is  the  distance  from  A 
to  P.  But  if  we  take  any  other  point  at  the  same  dis- 
tance from  A  its  potential  will  also  be  q/r.  Now  all  the 
points  that  are  the  same  distance  from  A  as  P  is,  will  be 
found  to  lie  upon  the  surface  of  a  sphere  whose  centre  is 
at  A,  and  which  is  represented  by  the  circle  drawn  through 
P,  in  Fig.  146.  All  round  this  circle  the  potential  will 
have  equal  values ;  hence  this  circle  represents  an  equi- 
potential  surface.  The  work  to  be  done  in  bringing  up 
a  +  unit  from  an  infinite  distance  will  be  the  same,  no 

*  The  student  must  be  warned  that  this  ceases  to  be  true  if  other 
charges  are  brought  very  near  to  the  sphere,  for  then  the  electricity  will 
no  longer  be  distributed  uniformly  over  its  surface.  It  is  for  this  reason 
that  we  have  said,  in  describing  the  measurement  of  electrical  forces  with 
the  torsion  balance,  that  "  the  balls  must  be  very  small  in  proportion  to 
the  distances  between  them." 


CHAP,  iv        EQUIPOTENTIAL   SURFACES  253 

matter  what  point  of  this  equipotential  surface  it  is 
brought  to,  and  to  move  it  about  from  one  point  to 
another  in  the  equipotential  surface  requires  no  further 
overcoming  of  the  electrical  forces,  and  involves  therefore 
no  further  expenditure  of  work.  At  another  distance, 
say  at  the  point  Q,  the  potential  will  have  another  value, 
and  through  this  point  Q  another  equipotential  surface 
may  be  drawn.  Suppose  we  chose  Q  so  far  from  P  that 
to  push  up  a  unit  of  -4-  electricity  against  the  repelling 
force  of  A  required  the  expenditure  of  just  one  erg  of 
work  (for  the  definition  of  one  erg  see  the  Note  on  Units 
at  the  end  of  this  lesson)  ;  there  will  be  then  unit 
difference  of  potential  between  the  surface  drawn  through 
Q  and  that  drawn  through  P,  and  it  will  require  one 
erg  of  work  to  carry  a  +  unit  from  any  point  on  the  one 
surface  to  any  point  on  the  other.  In  like  manner  we 
might  construct  a  whole  system  of  equipotential  surfaces 
about  the  point  A,  choosing  them  at  such  distances  that 
there  should  be  unit  difference  of  potential  between  each 
one  and  the  next.  The  widths  between  them  would  get 
wider  and  wider,  for,  since  the  force  falls  off  as  you 
go  further  from  A,  you  must,  in  doing  one  erg  of  work, 
bring  up  the  +  unit  through  a  longer  distance  against 
the  weaker  opposing  force. 

The  form  of  the  equipotential  surfaces  about  two  small 
electrified  bodies  placed  near  to  one  another  would  not 
be  spherical;  and  around  a  number  of  electrified  bodies 
placed  near  to  one  another  the  equipotential  surfaces 
would  be  highly  complex  in  form. 

268.  Lines  of  Force.  —  The  electric  force,  whether 
of  attraction  or  repulsion,  always  acts  across  the  equi- 
potential surfaces  in  a  direction  normal  to  the  surface. 
The  lines  which  mark  the  direction  of  the  resultant 
electric  forces  are  sometimes  called  lines  of  electric  force. 
In  the  case  of  the  single  electrified  sphere  the  lines  of 
force  would  be  straight  lines,  radii  of  the  system  of  equi- 
potential spheres.  In  general,  however,  lines  of  force  are 


254  ELECTRICITY  AND   MAGNETISM      TART  n 

curved ;  in  this  case  the  resultant  force  at  any  point 
would  be  in  the  direction  of  the  tangent  to  the  curve  at 
that  point.  Two  lines  of  force  cannot  cut  one  another, 
for  it  is  impossible ;  the  resultant  force  at  a  point  cannot 
act  in  two  directions  at  once.  The  positive  direction 
along  a  line  of  force  is  that  direction  in  which  a  small 
positively-charged  body  would  be  impelled  by  the  electric 
force  if  free  to  move.  A  space  bounded  by  a  number  of 
lines  of  force  is  sometimes  spoken  of  as  a  tube  of  force. 
All  the  space,  for  example,  round  a  small  insulated 
electrified  sphere  may  be  regarded  as  mapped  out  into  a 
number  of  conical  tubes,  each  having  their  apex  at  the 
centre  of  the  sphere.  The  total  electric  force  exerted 
across  any  section  of  a  tube  of  force  is  constant  wherever 
the  section  be  taken. 

269.  Potential  within  a  Closed  Conductor.  —  The 
experiments  related  in  Arts.  32  to  36  prove  most  con- 
vincingly that  there  is  no  electric  force  inside  a  closed 
conductor  due  to  charges  outside  or  on  the  surface  of  the  con- 
ductor. Now  we  have  shown  above  that  electric  force  is 
the  rate  of  change  of  potential  per  unit  of  length.  If 
there  is  no  electric  force  there  is  no  change  of  potential. 
The  potential  within  a  closed  conductor  (for  example,  a 
hollow  sphere)  due  to  charges  outside  or  on  the  surface 
is  therefore  the  same  all  over  the  interior ;  the  same  as 
the  potential  of  the  surface.  The  surface  of  a  closed  con- 
ductor is  necessarily  an  equipotential  surface.  If  it  were 
not  at  one  potential  there  would  be  a  flow  of  electricity 
from  the  higher  potential  to  the  lower,  which  would 
instantaneously  establish  equilibrium  and  reduce  the 
whole  to  one  potential.  The  student  should  clearly  dis- 
tinguish between  the  surface-density  at  a  point,  and  the 
potential  at  that  point  due  to  neighbouring  charges  of 
electricity.  We  know  that  when  an  electrified  body  is 
placed  near  an  insulated  conductor  the  nearer  and  farther 
portions  of  that  conductor  exhibit  induced  charges  of 
opposite  kinds.  Yet  all  is  at  one  potential.  If  the  + 


CHAP,  iv    POTENTIAL   INSIDE   CONDUCTORS         255 

and  —  charges  on  the  conductor  had  not  separated  by 
a  movement  of  electricity  from  one  side  to  the  other, 
a  difference  of  potential  would  exist  between  those  sides 
because  they  are  at  different  distances  from  the  electri- 
fied body.  But  that  is  a  state  of  affairs  which  could 
not  continue  in  the  conductor,  for  the  difference  of 
potential  would  cause  electricity  to  flow  until  the  com- 
bined potential  due  to  the  electrified  body  and  the  charges 
at  the  opposite  sides  was  the  same  at  every  point  in  the 
conductor. 

The  potential  at  any  point  in  a  conducting  sphere 
(hollow  or  solid)  due  to  an  electrified  particle  A,  situated 
at  a  point  outside  (Fig.  148),  is  equal  to  the  quantity  of 
electricity  q  at  A  divided  by  the  distance  between  A  and 
the  centre  of  the  sphere.  For  if  B  be  the  centre  of  the 
sphere,  the  potential  at  B  due  to  q  is  q/r,  where  r  =  AB ; 
but  all  points  in  the  sphere  are  at  the  same  potential, 
therefore  they  are  all  at  the  potential  q/r. 

The  earth  is  a  large  conducting  sphere.  Its  potential, 
due  to  a  positive  charge  q  near  to  its  surface,  is  q/r, 
where  r  may  be  taken  as  the  radius  of  the  earth ;  that 
is  636,000,000  centimetres.  But  it  is  impossible  to  pro- 
duce a  +  charge  q  without  generating  also  an  equal 
negative  charge  —  q]  so  the  potential  of  the  earth  due 
to  both  charges  is  q/r  —  q/r  =  0  (see  Art.  264). 

270.  Law  of  Inverse  Squares.  —  An  important  con- 
sequence follows  from  the  absence  of  electric  force  inside 
a  closed  conductor  due  to  a  charge  on  its  surface ;  this 
fact  enables  us  to  demonstrate  the  necessary  truth  of  the 
"  law  of  inverse  squares  "  which  was  first  experimentally, 
though  roughly,  proved  by  Coulomb  with  the  torsion 
balance.  Suppose  a  point  P  anywhere  inside  a  hollow 
sphere  charged  with  electricity  (Fig.  147).  The  charge 
is  uniform  all  over,  and  the  quantity  of  electricity  on 
any  small  portion  of  its  surface  will  be  proportional  to 
the  area  of  that  portion.  Consider  a  small  portion  of  the 
surface  AB.  The  charge  on  AB  would  repel  a  +  unit 


256  ELECTRICITY   AND   MAGNETISM      PART  n 

placed  at  P  with  a  certain  force.  Now  draw  the  lines 
AD  and  BC  through  P,  and  regard  these  as  mapping  out 
a  small  conical  surface  of  two  sheets,  having  its  apex  at 
P;  the  small  area  CD  will 
represent  the  end  of  the 
opposed  cone,  and  the  elec- 
tricity on  CD  will  also  act  on 
the  +  unit  placed  at  P,  and 
repel  it.  Now  these  surfaces 
AB  and  CD,  and  the  charges 
on  them,  will  be  directly  pro- 
portional to  the  squares  of 
their  respective  distances 
from  P.  If,  then,  the  forces 
which  they  exercise  on  P 

exactly  neutralize  one  another  (as  experiment  shows 
they  do),  it  is  clear  that  the  electric  force  must  fall  off 
inversely  as  the  squares  of  the  distances;  for  the  whole 
surface  of  the  sphere  can  be  mapped  out  similarly  by 
imaginary  cones  drawn  through  P.  The  reasoning  can 
be  extended  also  to  hollow  conductors  of  any  form. 

271.  Capacity.  —  In  Lesson  IV.  the  student  was 
given  some  elementary  notions  on  the  subject  of  the 
Capacity  of  conductors.  We  are  now  ready  to  give  the 
precise  definition.  The  Electrostatic  Capacity  of  a  con- 
ductor is  measured  by  the  quantity  of  electricity  ivhich  must 
be  imparted  to  it  in  order  to  raise  its  potential  from  zero  to 
unity.  A  small  conductor,  such  as  an  insulated  sphere 
of  the  size  of  a  pea,  will  not  want  so  much  as  one  unit 
of  electricity  to  raise  its  potential  from  0  to  1 ;  it  is 
therefore  of  small  capacity  —  while  a  large  sphere  will 
require  a  large  quantity  to  raise  its  potential  to  the  same 
degree,  and  would  therefore  be  said  to  be  of  large  capacity. 
If  K  stand  for  capacity,  and  Q  for  a  quantity  of  electricity, 

K  =  ^  and  KV  -  Q. 

This  is  equivalent  to  saying  in  words  that  the  quantity 


CAPACITIES   OF   SPHERES  257 


of  electricity  necessary  to  charge  a  given  conductor  to 
a  given  potential,  is  numerically  equal  to  the  product  of 
the  capacity  into  the  potential  through  which  it  is  raised. 
The  capacity  of  an  insulated  body  is  affected  by  the  pres- 
ence of  neighbouring  conductors.  Whenever  we  speak 
of  the  capacity  of  a  body,  we  mean  of  that  body  when 
isolated  as  well  as  insulated. 

272.  Unit  of  Capacity.  —  A  conductor  that  required 
only  one  unit  of  electricity  to  raise  its  potential  from  0  to 
1,  would  be  said  to  possess  unit  capacity.  A  sphere  one 
centimetre  in  radius  possesses  unit  capacity ;  for  if  it  be 
charged  with  a  quantity  of  one  unit,  this  charge  will 
act  as  if  it  were  collected  at  its  centre. 
At  the  surface,  which  is  one  centimetre 
away  from  the  centre,  the  potential, 
which  is  measured  as  q/r,  will  be  1. 
Hence,  as  1  unit  of  quantity  raises  it  to 
unit  1  of  potential,  the  sphere  possesses 
unit  capacity.  The  capacities  of  spheres  jrjg.  143. 

(isolated  in  air)  are  proportional  to  their 
radii.  We  may  imagine  the  charge  q  (Fig.  148)  being 
brought  nearer  and  nearer  the  sphere  until  it  reaches  the 
surface,  then  r  becomes  the  radius  of  the  sphere.  We 
may  further  imagine  the  surface  completely  covered 
with  little  quantities  q,  so  as  to  have  a  total  charge  Q 
uniformly  distributed.  Each  little  quantity  would  give 
to  the  sphere  a  potential  q/r ;  the  total  potential  of  the 
sphere  due  to  the  charge  Q,  on  its  surface  would  be  Q/r. 
The  greater  the  sphere  the  less  would  be  the  potential 
at  any  point  in  it  due  to  the  same  charge  Q.  Thus  it 
would  be  necessary  to  give  a  charge  of  100  units  to  a 
sphere  of  100  centimetres'  radius  in  order  to  raise  its 
potential  to  unity.  It  therefore  has  a  capacity  of  100. 
The  earth  has  a  capacity  of  about  630  millions  (in  electro- 
static units).*  It  is  almost  impossible  to  calculate  the 
capacities  of  conductors  of  other  shapes.  It  must  be  noted 

*  Or  about  700  microfarads  (see  Art.  283). 


258  ELECTRICITY   AND   MAGNETISM      PART  n 

that  the  capacity  of  a  sphere,  as  given  above,  means  its 
capacity  when  far  removed  from  other  conductors  or 
charges  of  electricity.  The  capacity  of  a  conductor  is 
increased  by  bringing  near  it  a  charge  of  an  opposite  kind; 
for  the  potential  at  the  surface  of  the  conductor  is  the  sum 
of  the  potential  due  to  its  own  charge,  and  of  the  potential 
of  opposite  sign  due  to  the  neighbouring  charge.  Hence, 
to  bring  up  the  resultant  potential  to  unity,  a  larger 
quantity  of  electricity  must  be  given  to  it ;  or,  in  other 
words,  its  capacity  is  greater.  This  is  the  true  way  of 
regarding  the  action  of  Leyden  jars  and  other  condensers, 
and  must  be  remembered  by  the  student  when  he  advances 
to  the  consideration  of  the  theory  of  condenser  action,  in 
Lesson  XXIII. 

273.  Surface-Density.*  —  Coulomb  applied  this  term 
to  denote  the  amount  of  electrification  per  unit  of  area 
at  any  point  of  a  surface.  It  was  mentioned  in  Lesson 
IV.  that  a  charge  of  electricity  was  never  distributed 
uniformly  over  a  conductor,  except  in  the  case  of  an 
insulated  sphere.  Where  the  distribution  is  unequal,  the 
density  at  any  point  of  the  surface  may  be  expressed  by 
considering  the  quantity  of  electricity  which  exists  upon 
a  small  unit  of  area  at  that  point.  If  Q  be  the  quantity 
of  electricity  on  the  small  surface,  and  S  be  the  area  of 
that  small  surface,  then  the  surface-density  (denoted  by 
the  Greek  letter  p)  will  be  given  by  the  equation, 

"4 

*  The  word  Tension  is  sometimes  used  for  that  which  is  here  precisely 
defined  as  Coulomb  defined  it.  The  term  tension  is,  however,  unfortunate  ; 
and  it  is  so  often  misapplied  in  text-books  to  mean  not  only  surface- 
density  but  also  potential,  and  even  electric  force  (i.e.  the  mechanical 
force  exerted  upon  a  material  body  by  electricity),  that  we  might  well 
avoid  its  use  altogether.  The  term  would  be  invaluable  if  we  might 
adopt  it  to  denote  only  the  mechanical  stress  across  a  dielectric,  as  in  Art. 
279.  This  was  Maxwell's  use  of  the  word,  denoting  a  pulling  force  dis- 
tributed over  an  area,  just  as  the  word  pressure  means  a  distributed 
pushing  force. 


CHAP,  iv      SURFACE   DENSITY   OF  CHARGES        259 

In  dry  air,  the  limit  to  the  possible  electrification  is 
reached  when  the  density  reaches  the  value  of  about  20 
units  of  electricity  per  square  centimetre.  If  charged  to 
a  higher  degree  than  this,  the  electricity  escapes  in 
"  sparks  "  and  "  brushes  "  into  the  air.  In  the  case  of 
uniform  distribution  over  a  surface  (as  with  the  sphere, 
and  as  approximately  obtained  on  a  flat  disk  by  a  par- 
ticular device  known  as  a  guard-ring),  the  density  is 
found  by  dividing  the  whole  quantity  of  the  charge  by 
the  whole  surface. 

274,  Surface-Density  on  a  Sphere.  —  The  surface 
of  a  sphere  whose  radius  is  r,  is  47rr2.  Hence,  if  a 
charge  Q  be  imparted  to  a  sphere  of  radius  r,  the  surface- 

density  all  over  will  be  p  =    ^    ;  or,  if  we  know  the 
surface-density,   the    quantity    of    the    charge    will    be 


The  surface-density  on  two  spheres  joined  by  a  thin 
wire  is  an  important  case.  If  the  spheres  are  unequal, 
they  will  share  the  charge  in  proportion  to  their  capacities 
(see  Art.  40),  that  is,  iri  proportion  to  their  radii.  If  the 
spheres  are  of  radii  2  and  1,  the  ratio  of  their  charges 
will  also  be  as  2  to  1.  But  their  respective  densities  will 
be  found  by  dividing  the  quantities  of  electricity  on  each 
by  their  respective  surfaces.  But  the  surfaces  are  pro- 
portional to  the  squares  of  the  radii,  i.e.  as  4:1;  hence, 
the  densities  will  be  as  1  :  2,  or  inversely  as  the  radii. 
Now,  if  one  of  these  spheres  be  very  small  —  no  bigger 
than  a  point  —  the  density  on  it  will  be  relatively 
immensely  great,  so  great  that  the  air  particles  in 
contact  with  it  will  rapidly  carry  off  the  charge  by 
convexion.  This  explains  the  action  of  points  in  dis- 
charging conductors,  noticed  in  Chapter  I.,  Arts.  38,  45, 
and  47. 

275.  Electric  Images  —  It  can  be  shown  mathe- 
matically that  if  +  q  units  of  electricity  are  placed  at  a 
point  near  a  non-insulated  conducting  sphere  of  radius 


260  ELECTRICITY  AND   MAGNETISM      PART  n 

r,  at  a  distance  d  from  its  centre,  the  negative  induced 
charge  will  be  equal  to  —  qr/d,  and  will  be  distributed 
over  the  nearest  part  of  the  surface  of  the  sphere  with  a 
surface-density  inversely  proportional  to  the  cube  of  the 
distance  from  that  point.  Lord  Kelvin  pointed  out  that, 
so  far  as  all  external  points  are  concerned,  the  potential 
due  to  this  peculiar  distribution  on  the  surface  would 
be  exactly  the  same  as  if  this  negative  charge  were  all 
collected  at  an  internal  point  at  a  distance  of  r  —  r^/d 
behind  the  surface.  Such  a  point  may  be  regarded  as  a 
virtual  image  of  the  external  point,  in  the  same  way  as  in 
optics  we  regard  certain  points  behind  mirrors  as  the 
virtual  images  of  the  external  points  from  which  the  rays 
proceed.  Clerk  Maxwell  has  given  the  following  defini- 
tion of  an  Electric  Image:  —  An  electric  image  is  an 
electrified  point,  or  system  of  points,  on  one  side  of  a  surface, 
which  would  produce  on  the  other  side  of  that  surface  the 
same  electrical  action  which  the  actual  electrification  of  that 
surface  really  does  produce.  If  the  sphere  is  not  connected 
to  earth,  and  were  unelectrified  before  +  q  was  brought 
near  it,  we  may  find  the  surf  ace- density  at  any  point  by  the 
following  convention.  Imagine  that  there  are  coexisting 
on  the  sphere  two  charges,  —  rq/d  and  +  rg/d  respec- 
tively, the  first  being  distributed  so  that  its  surface-density 
is  inversely  proportional  to  the  cube  of  the  distance  from 
the  electrified  point,  and  the  second  being  uniformly 
distributed.  The  actual  surface-density  is  the  algebraic 
sum  of  these  two.  A  +  charge  of  electricity  placed  1 
inch  in  front  of  a  flat  metallic  plate  induces  on  it  a  nega- 
tive charge  distributed  over  the  neighbouring  region  of 
the  plate  (with  a  density  varying  inversely  as  the  cube 
of  the  distance  from  the  point) ;  but  the  electrical  action 
of  this  distribution,  so  far  as  all  points  in  front  of  the 
plate  are  concerned,  would  be  precisely  represented  by 
its  "image,"  namely,  by  an  equal  quantity  of  nega- 
tive electricity  placed  at  a  point  1  inch  behind  the 
plate.  Many  beautiful  mathematical  applications  of  this 


CHAP,  iv      FORCE   NEAR   CHARGED   SPHERE        261 

method  have  been  made,  enabling  the  distribution  to  be 
calculated  in  difficult  cases,  as,  for  example,  the  distri- 
bution of  the  charge  on  the  inner  surface  of  a  hollow 
bowl. 

276.  Force  near  a  Charged  Sphere.  —  It  was  shown 
above  that  the  quantity  of  electricity  Q  upon  a  sphere 
charged  until  its  surface-density  was  p,  was 


Q  - 

The  problem  is  to  find  the  force  exercised  by  this 
charge  upon  a  +  unit  of  electricity,  placed  at  a  point 
infinitely  near  the  surface  of  the  sphere.  The  charge  on 
the  sphere  acts  as  if  at  its  centre.  The  distance  between 
the  two  quantities  is  therefore  r.  By  Coulomb's  Law  the 

,  .      Qxl 

force/  =  —  ^- 

This  important  result  may  be  stated  in  words  as 
follows  :  —  The  force  (in  dynes)  exerted  by  a  charged  sphere 
upon  a  unit  of  electricity  placed  infinitely  near  to  its  surface, 
is  numerically  equal  to  4?r  times  the  surface-density  of  the 
charge. 

277.  Force  near  a  Charged  Plate  of  indefinite  size.  — 
Suppose  a  plate  of  indefinite  extent  to  be  charged  so 
that  it  has  a  surface-density  p.  This  surface-density 
will  be  uniform,  for  the  edges  of  the  plate  are  supposed 
to  be  so  far  off  as  to  exercise  no  influence.  It  can  be 
shown  that  the  force  exerted  by  such  a  plate  upon  a  + 
unit  anywhere  near  it,  will  be  expressed  (in  dynes)  numeri- 
cally as  2?rp.  This  will  be  of  opposite  signs  on  opposite 
sides  of  the  plate,  being  +  2?rp  on  one  side,  and  —  2?rp 
on  the  other  side,  since  in  one  case  the  force  tends  to 
move  the  unit  from  right  to  left,  in  the  other  from  left 
to  right.  It  is  to  be  observed,  therefore,  that  the  force 
changes  its  value  by  the  amount  of  4?rp  as  the  point 
passes  through  the  surface.  The  same  was  true  of  the 
charged  sphere,  where  the  force  outside  was  47rp,  and 
inside  was  zero.  The  same  is  true  of  all  charged  sur- 


262  ELECTRICITY  AND   MAGNETISM      PART  n 

faces.     These  two  propositions  are  of  the  utmost  impor- 
tance in  the  theory  of  Electrostatics. 

278.   Proof  of  Theorem.  —  The  elementary  geometri- 
cal proof  is  as  follows  :  — 

Required  the  Electric  Force  at  point  at  any  distance  from  a 

plane  of  infinite  extent  charged  to  surface-density  p. 
Let  P  be  the  point,  and  PX  or  a  the  normal  to  the  plane. 
Take  any  small  cone  having  its  apex  at  P.     Let  the  solid  angle 
of  this  cone  be  u> ;  let  its  length  be  r ;  and  9  the  angle  its  axis 


makes  with  a.  The  cone  meets  the  surface  of  the  plane  obliquely, 
and  if  an  orthogonal  section  be  made  where  it  meets  the  plane, 
the  angle  between  these  sections  will  be  =  0. 

orthogonal  area  of  section 
Now  solid  angle  «  is  by  definition  =  -  —  —  — 

Hence,  area  of  oblique  section  =  7-2a>  x  -  ; 

cos  e 

?^tOD 

.*.  charge  on  oblique  section  =  --  ~. 

COS  u 

Hence  if  a  +  unit  of  electricity  were  placed  at  P,  the  force 
exerted  on  this  by  this  small  change  =  —  ^  X  1  •*•  r2, 


Resolve  this  force  into  two  parts,  one  acting  along  the  plane, 
the  other  along  «,  normal  to  the  plane.    The  normal  component 

along  a  is  cos  e  x 


CHAP,  iv    ELECTRIC   STRESS  IN  MEDIUM  263 


But  the  whole  surface  of  the  plane  may  be  similarly  mapped 
out  into  small  surfaces,  all  forming  small  cones,  with  their  sum- 
mits at  P.  If  we  take  an  infinite  number  of  such  small  cones 
meeting  every  part,  and  resolve  their  forces  in  a  similar  way, 
we  shall  find  that  the  components  along  the  plane  will  neutral- 
ize one  another  all  round,  while  the  normal  components,  or  the 
resolved  forces  along  a,  will  be  equal  to  the  sum  of  all  their  solid 
angles  multiplied  by  the  surface-density ;  or 

Total  resultant  force  along  a  =  2wp. 

But  the  total  solid  angle  subtended  by  an  indefinite  plane  at 
a  point  is  2n,  for  it  subtends  a  whole  hemisphere. 

.  • .  Total  resultant  force  =  2n-p. 

279.  Electric  Stress  in  Medium.  —  In  every  electric 
field  (Art.  13)  there  exists  a  tension  along  the  lines  of 
electric  force  accompanied  by  an  equal  pressure  in  all 
directions  at  right  angles  to  the  lines.  If  F  stands  for 
the  resultant  electric  force  on  a  +  unit  placed  at  any 
point  in  the  field  (i.e.  the  "electromotive  intensity"  at 
that  point),  the  tension  will  be  equal  to  F2/87r  (dynes  per 
square  centimetre).  In  media  having  dielectric  capacities 
greater  than  unity  the  tension  is  proportionately  greater. 
For  the  optical  effects  of  these  stresses  see  Art.  525. 


NOTE  ON  FUNDAMENTAL  AND  DERIVED  UNITS 

28O.  Fundamental  Units.  —  All  physical  qualities,  such  as 
force,  velocity,  etc.,  can  be  expressed  in  terms  of  the  three 
fundamental  quantities:  length,  mass,  and  time.  Each  of  these 
quantities  must  be  measured  in  terms  of  its  own  units. 

The  system  of  units,  adopted  by  almost  universal  consent, 
and  used  throughout  these  lessons,  is  the  so-called  "  Centi- 
metre-Gramme-Second"  system,  in  which  the  fundamental 
units  are :  — 

The  Centimetre  as  a  unit  of  length ; 

The  Gramme  as  a  unit  of  mass  ; 

The  Second  as  a  unit  of  time. 

The  Centimetre  is  equal  to  0'3937  inch  in  length,  and  nomi- 


264  ELECTRICITY   AND   MAGNETISM      PART  n 


nally  represents  one  thousand-millionth  part,  or  ,-juj       ^  of 


quadrant  of  the  earth. 

The  Metre  is  100  centimetres,  or  39*37  inches. 

The  Kilometre  is  1000  metres,  or  about  1093'G  yards. 

The  Millimetre  is  &  of  a  centimetre,  or  0'03937  inch. 

The  Gramme  represents  the  mass  of  a  cubic  centimetre  of 
water  at  4°C.,  this  is  equal  to  15-432  grains:  the  Kilogramme  is 
1000  grammes  or  about  2'2  pounds. 

281.  Derived  Units.— 

Area.  —  The  unit  of  area  is  the  square  centimetre. 

Volume.  —  The  unit  of  volume  is  the  cubic  centimetre. 

Velocity.  —  The  unit  of  velocity  is  the  velocity  of  a  body 
which  moves  through  unit  distance  in  unit  time,  or  the 
velocity  of  one  centimetre  per  second. 

Acceleration.  —  The  unit  of  acceleration  is  that  acceleration 
which  imparts  unit  velocity  to  a  body  in  unit  time,  or 
an  acceleration  of  one  centinietre-per-secoud  per  second. 
The  acceleration  due  to  gravity  imparts  in  one  second  a 
velocity  considerably  greater  than  this,  for  the  velocity 
it  imparts  to  falling  bodies  is  about  981  centimetres  per 
second  (or  about  32-2  feet  per  second) .  The  value  differs 
slightly  in  different  latitudes.  At  Greenwich  the  value 
of  the  acceleration  of  gravity  is  g  =  981'1 ;  at  the  Equa- 
tor g  =  978'1 ;  at  the  North  Pole  g  =  983-1. 

Force.  — The  unit  of  force  is  that  force  which,  acting  for  one 
second  on  a  mass  of  one  gramme,  gives  to  it  a  velocity 
of  one  centimetre  per  second.  It  is  called  one  Dyne. 
The  force  with  which  the  earth  attracts  any  mass  is 
usually  called  the  "  weight "  of  that  mass,  and  its  value 
obviously  differs  at  different  points  of  the  earth's  sur- 
face. The  force  with  which  a  body  gravitates,  i.e.  its 
weight  (in  dynes),  is  found  by  multiplying  its  mass  (in 
grammes)  by  the  value  of  g  at  the  particular  place  where 
the  force  is  exerted.  One  pound  force  in  England  is 
about  445,000  dynes. 

Work.  —  The  unit  of  work  is  the  work  done  in  overcoming 
unit  force  through  unit  distance,  i.e.  in  pushing  a  body 
through  a  distance  of  one  centimetre  against  a  force  of 
one  dyne.  It  is  called  one  Erg.  Since  the  "weight "  of 
one  gramme  is  1x981  or  981  dynes,  the  work  of  raising 
one  gramme  through  the  height  of  one  centimetre  against 
the  force  of  gravity  is  981  ergs. 

Energy.  —  The  unit  of  energy  is  also  the  erg ,'  for  the  energy 
of  a  body  is  measured  by  the  work  it  can  do. 


CHAP,  iv  ELECTROSTATIC   UNITS  265 


Heat.  —  The  unit  of  heat,  the  calorie,  is  the  amount  of  heat 
required  to  warm  one  gramme  mass  of  water  from  0°  to 
1°  (C.) ;  and  the  dynamical  equivalent  of  this  amount  of 
heat  is  42  million  ergs,  which  is  the  value  of  Joule's  equi- 
valent, as  expressed  in  C.G.S.  measure  (see  also  Art.  439) . 

These  units  are  sometimes  called  "absolute"  units;  the 
term  absolute,  introduced  by  Gauss,  meaning  that  they  are 
independent  of  the  size  of  any  particular  instrument,  or  of  the 
value  of  gravity  at  any  particular  place,  or  of  any  other  arbi- 
trary quantities  than  the  three  standards  of  length,  mass,  and 
time.  It  is,  however,  preferable  to  refer  to  them  by  the  more 
appropriate  name  of  "  C.G.S.  units,"  as  being  derived  from  the 
centimetre,  the  gramme,  and  the  second. 

282.  Electrical  Units.  —  There  are  two  systems  of  electrical 
units  derived  from  the  fundamental  "  C.G.S."  units,  one  set 
being  based  upon  the  force  exerted  between  two  quantities  of 
electricity,  and  the  other  upon  the  force  exerted  between  two 
magnet  poles.    The  former  set  are  termed  electrostatic  units,  the 
latter  electro-magnetic  units.    The  important  relation  between 
the  two  sets  is  explained  in  Art.  359. 

283.  Electrostatic  Units.  —  No  special  names  have  been 
assigned    to    the    electrostatic    units    of  Quantity,    Potential, 
Capacity,  etc.    The  reasons  for  adopting  the  following  values 
as  units  are  given  either  in  Chapter  I.  or  in  the  present  chapter. 

Unit  of  Quantity.  —  The  unit  of  quantity  is  that  quantity 
of  electricity  which,  when  placed  at  a  distance  of  one 
centimetre  (in  air)  from  a  similar  and  equal  quantity, 
repels  it  with  a  force  of  one  dyne  (Art.  262). 

Potential.  —  Potential  being  measured  by  work  done  in  mov- 
ing a  unit  of  -f-  electricity  against  the  electric  forces,  the 
unit  of  potential  will  be  measured  by  the  unit  of  work, 
the  erg. 

Unit  Difference  of  Potential.  —  Unit  difference  of  potential 
exists  between  two  points,  when  it  requires  the  expendi- 
ture of  one  erg  of  work  to  bring  a  -f-  unit  of  electricity 
from  one  point  to  the  other  against  the  electric  force 
(Art.  265). 

Unit  of  Capacity.  —  That  conductor  possesses  unit  capacity 
which  requires  a  charge  of  one  unit  of  electricity  to 
bring  it  up  to  unit  potential.  A  sphere  of  one  centi- 
metre radius  possesses  unit  capacity  (Art.  272). 

Specific  Inductive  Capacity,  or  Dielectric  Coefficient,  is  de- 
fined in  Art.  295  as  the  ratio  between  two  quantities  of 
electricity.  The  specific  inductive  capacity  of  the  air 


266  ELECTRICITY  AND   MAGNETISM      PART  n 

is,  in  the  absence  of  any  knowledge  of  its  absolute 
value,  taken  as  unity. 

Electromotive  Intensity  is  the  electric  force  or  intensity  of  an 
electric  field  at  any  point,  and  is  measured  by  the  force 
which  it  exerts  on  a  unit  charge  placed  at  that  point. 

It  may  be  convenient  here  to  append  the  rules  for  re- 
ducing to  their  corresponding  values  in  terms  of  the  prac- 
tical (electro-magnetic)  units  values  that  may  have  been 
expressed  in  terms  of  the  electrostatic  units,  as  follows  :  — 

Potential.      To  bring  to  volts  multiply  by  300. 
Capacity.       To  bring  to  microfarads  divide  by  900,000. 
Quantity.       To  bring  to  coulombs  divide  by  3  X  109. 
Current.         To  bring  to  amperes  divide  by  3  X  109. 
Resistance.    To  bring  to  ohms  multiply  by  9  X  1011. 
Example.  —  Suppose  two  equally  charged  spheres  whose  centres  arc 
40  centimetres  apart  are  found  to  repel  one  another  with  a  force 
of  630  dynes  (=  about  the  weight  of  10  grains).    By  the  law  of 
inverse  squares  we  find  that  the  charge  on  eacli  is  1004  (electro- 
static units.    Dividing  by  3  x  109  we  find  that  this  amounts  to 
0-0000003347  coulomb. 

284.  Dimensions  of  Units.  —  It  has  been  assumed  above 
that  a  velocity  can  be  expressed  in  centimetres  per  second ;  for 
velocity  is  rate  of  change  of  place,  and  it  is  clear  that  if  change 
of  place  may  be  measured  as  a  length  in  centimetres,  the  rate 
of  change  of  place  will  be  measured  by  the  number  of  centi- 
metres through  which  the  body  moves  in  unit  of  time.  It  is 
impossible,  indeed,  to  express  a  velocity  without  regarding  it  as 
the  quotient  of  a  certain  number  of  units  of  length  divided  by 
a  certain  number  of  units  of  time.  In  other  words,  a  velocity 

=  t.  ;  or,  adopting  L  as  a  symbol  for  length,  and  T  as  a 
symbol  for  time,  V  =  -,  which  is  still  more  conveniently  written 
V  =  L  X  T  -1.  In  a  similar  way  acceleration  being  rate  of 
change  of  velocity,  we  have  A  =  -  = =  -^  =  L  x  T  --. 

Now  these  physical  quantities, "  velocity  "  and  "  acceleration," 
are  respectively  always  quantities  of  the  same  nature,  no  matter 
whether  the  centimetre,  or  the  inch,  or  the  mile,  be  taken  as  the 
unit  of  length,  or  the  second  or  any  other  interval  be  taken  as 
the  unit  of  time.  Hence  we  say  that  these  abstract  equations 
express  the  dimensions  of  those  quantities  with  respect  to  the 
fundamental  quantities  length  and  time.  A  little  consideration 


CHAP.    IV 


DIMENSIONS   OF  UNITS 


267 


will  show  the  student  that  the  dimensions  of  the  various  units 
mentioned  above  will  therefore  be  as  given  in  the  table  below. 

The  dimensions  of  magnetic  units  are  given  in  the  Table  in 
Art.  356,  p.  348. 

TABLE  OF  DIMENSIONS  OF  UNITS. 


UNITS. 

DIMENSIONS. 

(Fundamental) 

I 

Length 

L 

m 

Mass 

M 

t 

Time 

T 

(Derived) 

Area              =                L  x  L 

L2 

Volume         =                L  x  L  x  L 

L3 

V 

Velocity        =                L4T 

LT"1 

a 

Acceleration  =  velocity  4  time 

LT~2 

f 

Force             =  mass  x  acceleration 

MLT~2 

"Work             =  force  x  length 

MLT-* 

(Electrostatic) 

q 

Quantity                =*^force  x  (distance)2        = 

M*  Li  T"1 

i 

Current                  =  quantity  4  time 

Mi  Li  T~2 

V 

Potential                =  work  4  quantity 

Mil^T"1 

B 

Resistance             =  potential  4  current         = 

L-!Ti 

c 

Capacity                =  quantity  4  potential       = 

L 

k 

Sp.  Ind.  Capacity  =  quantity  4  another  quantity 

a  numeral 

F 

Electromotive  Intensity  =  force  4-  quantity  = 

MlLJT-' 

LESSON  XXII.  — Electrometers 

285.  In  Lesson  II.  we  described  a  number  of  electro- 
scopes or  instruments  for  indicating  the  presence  and 
sign  of  a  charge  of  electricity ;  some  of  these  also  served 


268  ELECTRICITY  AND   MAGNETISM      PART  11 

to  indicate  roughly  the  amount  of  these  charges,  but 
none  of  them  save  the  torsion  balance  could  be  regarded 
as  affording  an  accurate  means  of  measuring  either  the 
quantity  or  the  potential  of  a  given  charge.  An  instru- 
ment for  measuring  differences  of  electrostatic  potential  is 
termed  an  Electrometer.  Such  instruments  can  also  be 
used  to  measure  electric  quantity  indirectly,  for  the 
quantity  of  a  charge  can  be  ascertained  by  measuring 
the  potential  to  which  it  can  raise  a  conductor  of  known 
capacity.  The  earliest  electrometers  attempted  to  meas- 
ure the  quantities  directly.  Lane  and  Snow  Harris 
constructed  "  Unit  Jars  "  or  small  Ley  den  jars,  which, 
in  order  to  measure  out  a  certain  quantity  of  electri- 
city, were  charged  and  discharged  a  certain  number  of 
times. 

286.  Repulsion  Electrometers.  —  The  torsion  balance, 
described  in  Art.  18,  measures  quantities  by  measuring 
the  forces  exerted  by  the  charges  given  to  the  fixed  and 
movable  balls.  It  can  only  be  applied  to  the  measure- 
ment of  repelling  forces,  for  the  equilibrium  is  unstable 
in  the  case  of  a  force  of  attraction. 

Beside  the  gold-leaf  electroscope  and  others  described 
in  Lesson  II.,  there  exist  several  finer  electrometers  based 
upon  the  principle  of  repulsion,  some  of  which  resemble 
the  torsion  balance  in  having  a  movable  arm  turning 
about  a  central  axis.  Amongst  these  are  the  electrometers 
of  Dellmann  and  of  Peltier.  In  the  latter  a  light  arm 
of  aluminium,  balanced  upon  a  point,  carries  also  a  small 
magnet  to  direct  it  in  the  magnetic  meridian.  A  fixed 
arm,  in  metallic  contact  with  the  movable  one,  also  lies 
in  the  magnetic  meridian.  A  charge  imparted  to  this 
instrument  produces  a  repulsion  between  the  fixed  and 
movable  arms,  causing  an  angular  deviation.  Here,  how- 
ever, the  force  is  measured  not  by  being  pitted  against 
the  torsion  of  an  elastic  fibre,  or  against  gravitation,  but 
against  the  directive  magnetic  force  of  the  earth  acting 
on  the  small  needle.  Now  this  depends  011  the  intensity 


CHAP,  iv  ELECTROMETERS  269 

of  the  horizontal  component  of  the  earth's  magnetism 
at  the  place,  on  the  magnetic  moment  of  the  needle, 
and  on  the  sine  of  the  angle  of  its  deviation.  Hence, 
to  obtain  quantitative  values  for  the  readings  of  this 
electrometer,  it  is  necessary  to  make  preliminary  experi- 
ments and  to  "calibrate"  the  degree-readings  of  the 
deviation. 

287.  Attracted  -  Disk  Electrometers.  —  Snow  Harris 
was  the  first  to  construct  an  electrometer  for  measur- 
ing the  attraction  between  an  electrified  and  a  non- 
electrified  disk;  and  the  instrument  he  devised  may 
be  roughly  described  as  a  balance  for  weighing  a  charge 
of  electricity.  More  accurately  speaking,  it  was  an  in- 
strument resembling  a  balance  in  form,  carrying  at  one 
end  a  light  scale  pan ;  at  the  other  a  disk  was  hung 
above  a  fixed  insulated  disk,  to  which  the  charge  to  be 
measured  was  imparted.  The  chief  defect  of  this  instru- 
ment was  the  irregular  distribution  of  the  charge  on  the 
disk.  The  force  exerted  by  an  electrified  point  falls  •  oif 
inversely  as  the  square  of  the  distance,  since  the  lines 
of  force  emanate  in  radial  lines.  But  in  the  case  of  a 
uniformly  electrified  plane  surface,  the  lines  of  force  are 
normal  to  the  surface,  and  parallel  to  one  another ;  and 
the  force  is  independent  of  the  distance.  The  distribu- 
tion over  a  small  sphere  nearly  fulfils  the  first  of  these 
conditions.  The  distribution  over  a  flat  disk  would 
nearly  fulfil  the  latter  condition,  were  it  not  for  the 
perturbing  effect  of  the  edges  of  the  disk  where  the 
surf  ace -density  is  much  greater  (see  Art.  38);  for 
this  reason  Snow  Harris's  electrometer  was  very  im- 
perfect. 

Lord  Kelvin  introduced  several  very  important  modifi- 
cations into  the  construction  of  attracted-disk  electro- 
meters, the  chief  of  these  being  the  employment  of  the 
"  guard-plate "  and  the  providing  of  means  for  work- 
ing with  a  definite  standard  of  potential.  It  would  be 
beyond  the  scope  of  these  lessons  to  give  a  complete 


270  ELECTRICITY   AND   MAGNETISM       PART  n 

description  of  all  the  various  forms  of  attracted-disk 
electrometer ;  *  but  the  main  principles  of  them  all  can 
be  readily  explained. 

The  disk  C,  whose  attraction  is  to  be  measured,  is 
suspended  (Fig.  150)  within  a  fixed  guard-plate  B,  which 
surrounds  it  without  touching  it,  and  which  is  placed  in 
metallic  contact  with  it  by  a  fine  wire.  A  Lever  L 
supports  the  disk,  and  is  furnished  with  a  counterpoise. 
In  order  to  know  whether  the  disk  is  precisely  level  with 
the  lower  surface  of  the  guard-plate  a  little  gauge  or  index 


Fig.  150. 

is  fixed  above,  and  provided  with  a  lens  I  to  observe  its 
indications.  Beneath  the  disk  and  guard-plate  is  a  second 
disk  A,  supported  on  an  insulating  stand.  This  lower 
disk  can  be  raised  or  lowered  at  will  by  a  micrometer 
screw,  great  care  being  taken  in  the  mechanical  arrange- 
ments that  it  shall  always  be  parallel  to  the  plane  of  the 
guard-plate.  Now,  since  the  disk  and  guard-plate  are  in 
metallic  connexion  with  one  another,  they  form  virtually 
part  of  one  surface,  and  as  the  irregularities  of  distribution 

*  For  these  the  student  is  referred  to  the  volume  of  Lord  Kelvin's 
papers,  "  On  Electrostatics  and  Magnetism  "  ;  or  to  Professor  Andrew 
Gray's  Absolute  Measurements  in  Electricity  and  Magnetism. 


CHAP,  iv    ATTRACTED-DISK  ELECTROMETERS    271 

occur  at  the  edges  of  the  surface,  the  distribution  over  the 
area  of  the  disk  is  practically  uniform.  Any  attraction  of 
the  lower  plate  upon  the  disk  might  be  balanced  either  by 
increasing  the  weight  of  the  counterpoise,  or  by  putting  a 
torsion  on  the  aluminium  wire  which  serves  as  a  fulcrum  ; 
but  in  practice  it  is  found  most  convenient  to  obtain  a 
balance  by  altering  the  distance  of  the  lower  plate  until 
the  electric  force  of  attraction  exactly  balances  the  forces 
(whether  of  torsion  or  of  gravity  acting  on  the  counter- 
poise) which  tend  to  lift  the  disk  above  the  level  of  the 
guard-plate. 

The  theory  of  the  instrument  is  simple  also.  Let  Vx 
represent  the  potential  of  the  movable  disk,  which  has  a 
positive  charge  of  surface-density  p,  and  let  V2  be  the 
potential  of  the  fixed  plate,  upon  which  is  a  charge 
of  surface-density  —  p.  The  difference  of  potential 
Vj  —  V2  is  the  work  which  would  have  to  be  done  upon 
a  unit  of  positive  charge  in  taking  it  from  V2  to  Vr 
Now  the  force  upon  such  a  unit  placed  between  the  two 
plates  would  be  (an  attraction  of  2  Trp  due  to  the  fixed 
plate,  and  a  repulsion  of  2  irp  due  to  the  movable  plate, 
see  Art.  278)  altogether  4  Trp,  and  if  the  distance  between 
the  plates  were  D.  Work  =  force  x  distance. 


If  S  is  the  area  of  the  movable  plate,  Sp  is  the  total 
quantity  of  electricity  on  it  ;  therefore  it  would  be 
attracted  by  the  fixed  plate  with  a  force  F  =  2  ?rp  x  Sp. 
From  this  we  get 


Substituting  this  value  of  p  in  the  above  equation,  we  get 


If  F  is  measured  in  dynes,  S  in  square  centimetres,  and 
D  in  centimetres,  the  potentials  will  be  in  absolute  electro- 


272  ELECTRICITY   AND   MAGNETISM 


static  units,  and  must  be  multiplied  by  300  to  bring  to 
volts  (see  Art.  283). 

From  this  we  gather  that,  if  the  force  F  remains  the 
same  throughout  the  experiments,  the  difference  of  poten- 
tials between  the  disks  will  be  simply  proportional  to  the  dis- 
tance between  them  when  the  disk  is  in  level  equilibrium. 

And  the  quantity    \— — —  may  be  determined  once  for 

S 

all  as  a  "  constant "  of  the  instrument. 

In  the  more  elaborate  forms  of  the  instrument,  such 
as  the  "  absolute  electrometer,"  and  the  "  portable 
electrometer,"  the  disk  and  guard-plate  are  covered 
with  a  metallic  cage,  and  are  together  placed  in  com- 
munication with  a  condenser  to  keep  them  at  a  known 
potential.  This  obviates  having  to  make  measurements 
with  zero  readings,  for  the  differences  of  potential  will 
now  be  proportional  to  differences  of  micrometer  readings, 


Vx  -  V2  =  (D,  -  D2)  . 

The  condenser  is  provided  in  these  instruments  with 
a  gauge,  itself  an  attracted  disk,  to  indicate  when  it  is 
charged  to  the  right  potential,  and  with  a  replenisher  to 
increase  or  decrease  the  charge,  the  replenisher  being  a 
little  influence  machine  (see  Art.  50). 

288.  The  Quadrant  Electrometer.  —  The  Quadrant 
Electrometer  of  Sir  W.  Thomson  is  an  example  of  a 
different  class  of  electrometers,  in  which  use  is  made  of 
an  auxiliary  charge  of  electricity  previously  imparted  to 
the  needle  of  the  instrument.  The  needle,  which  con- 
sists of  a  thin  flat  piece  of  aluminium  hung  horizontally 
by  a  fibre  of  thin  wire,  thus  charged,  say  positively,  will 
be  attracted  by  a  -  charge,  but  repelled  by  a  +  charge. 
Such  attraction  or  repulsion  will  be  stronger  in  proportion 
to  these  charges,  and  in  proportion  to  the  charge  on  the 
needle.  Four  quadrant-pieces  (Fig.  151)  of  brass  are  fixed 


CHAP,  iv       QUADRANT   ELECTROMETER  273 

horizontally  below  the  needle  without  touching  it  or  one 
another.  Opposite  quadrants  are  joined  with  fine  wires. 
If  quadrants  1  and  3  are  ever  so  little  +  as  compared 
with  quadrants  2  and  4,  the  needle  will  turn  away  from 
the  former  to  a  position  more  nearly  over  the  latter. 

If  there  is  the  slightest  difference  of  potential  between 
the  pairs  of  quadrants,  the  needle,  which  is  held  in  its 
zero  position  by  the  elasticity  of  the 
wire,  will  turn,  and  so  indicate  the 
difference  of  potential.  When  these 
deflexions  are  small,  the  scale  readings 
will  be  very  nearly  proportional  to  the 
difference  of  potential.  The  instru- 
ment is  sufficiently  delicate  to  show  a 
difference  of  potential  between  the 
quadrants  as  small  as  the  7^  of  that 
of  the  DanielFs  cell.  If  Vt  be  the  potential  of  one  pair  of 
quadrants,  V2  that  of  the  other  pair,  and  V3  the  potential 
of  the  needle,  the  force  tending  to  turn  will  be  proportional 
to  Vj  —  V2,  and  will  also  be  proportional  to  the  difference 
between  V3  and  the  average  of  Vx  and  V2.  Or,  in 
symbols, 


where  a  is  a  constant  depending  on  the  construction  of 
the  particular  instrument. 

Fig.  152  shows  a  very  simple  form  of  the  Quadrant 
Electrometer,  as  arranged  for  qualitative  experiments. 
The  four  quadrants  are  enclosed  within  a  glass  case,  and 
the  needle,  which  carries  a  light  mirror  M  below  it,  is 
suspended  from  a  torsion  head  C  by  a  very  thin  metallic 
wire  F.  It  is  electrified  to  a  certain  potential  by  being 
connected,  through  a  wire  attached  to  C,  with  a  charged 
Leyden  jar  or  other  condenser.  In  order  to  observe  the 
minutest  motions  of  the  needle,  a  reading-telescope  and 
scale  are  so  placed  that  the  observer  looking  through  the 
T 


274 


ELECTRICITY   AND   MAGNETISM 


telescope  sees  an  image  of  the  zero  of  the  scale  reflected 
in  the  little  mirror.  The  wires  connecting  quadrants  1 
and  3,  2  and  4,  are  seen  above  the  top  of  the  case. 

For  very  exact  measurements  many  additional  refine- 
ments are  introduced  into  the  instrument.     Two  sets  of 
quadrants  are  employed,  an  upper  and  a  lower,  having 
the  needle  between  them.     The  torsion  wire  is  replaced 
by  a  delicate  bifilar  suspension  (Art.  130). 
To  keep  up  the  charge  of  the  Leyden  jar  a 
"  replenisher  "  is  added ;  and  an  "  attracted- 
disk,"  like  that   of   the   Absolute   Electro- 
meter, is   employed   in   order   to   act   as   a 
gauge  to  indicate  when  the  jar  is  charged 
to  the  right  potential.     In  these  forms  the 
jar  consists  of  a  glass  vessel  placed  below 
the  quadrants,  coated  externally  with  strips 
of  tinfoil,  and  containing  strong  sulphuric 
acid,  which  serves  the  double  function  of 


Fig.  152. 


keeping  the  apparatus  dry  by  absorbing  the  moisture 
and  of  acting  as  an  internal  coating  for  the  jar.  It  is 
also  more  usual  to  throw  a  spot  of  light  from  a  lamp 
upon  a  scale  by  means  of  the  little  mirror  (as  described  in 
the  case  of  the  Mirror  Galvanometer,  in  Art.  215),  than 
to  adopt  the  subjective  method  with  the  telescope,  which 
only  one  person  at  a  time  can  use.  When  the  instrument 
is  provided  with  replenisher  and  gauge,  the  measurements 


CHAP,  iv      ELECTROSTATIC   VOLTMETER  275 

can  be  made  in  terms  of  absolute  units,  provided  the  "  con- 
stant "  of  the  particular  instrument  (depending  on  the 
suspension  of  the  needle,  size  and  position  of  needle  and 
quadrants,  potential  of  the  gauge,  etc.)  is  once  ascertained. 

289.  Use   of  Quadrant   Electrometer.  —  An  example  will 
illustrate  the  mode  of  using  the  instrument.    It  is  known  that 
when  the  two  ends  of  a  thin  wire  are  kept  at  two  different 
potentials  a  current  flows  through  the  wire,  and   that  if  the 
potential  is  measured  at  different  points   along  the  wire,  it  is 
found  to  fall  off  in  a  perfectly  uniform  manner  from  the  end 
that  is  at  a  high  potential  down  to  that  at  the  low  potential.   At 
a  point  one  quarter  along  the  potential  will  have  fallen  off  one 
quarter  of  the  whole  difference.      This  could  be  proved  by  join- 
ing the  two  ends  of  the  wire  through  which  the  current  was 
flowing  to  the  terminals  of  the  Quadrant  Electrometer,  when  one 
pair  of  quadrants  would  be  at  the  high  potential  and  the  other 
at  the  low  potential.    The  needle  would  turn  and  indicate  a  cer- 
tain deflexion.    Now,  disconnect  one  of  the  pairs  of  quadrants 
from  the  low  potential  end  of  the  wire,  and  place  them  in  com- 
munication with  a  point  one  quarter  along  the  wire  from  the 
high  potential  end.    The  needle  will  at  once  indicate  that  the 
difference  of  potential  is  but  one  quarter  of  what  it  was  before. 

Often  the  Quadrant  Electrometer  is  employed  simply  as  a 
very  delicate  electroscope  in  systems  of  measurement  in  which 
a  difference  of  electric  potential  is  measured  by  being  balanced 
against  an  equal  and  opposite  difference  of  potential,  exact  bal- 
ance being  indicated  by  there  being  no  deflexion  of  the  Electro- 
meter needle.  Such  methods  of  experimenting  are  known  as 
Xull  Mvtkodx,  or  Zero  Methods. 

290.  Electrostatic  Voltmeter.  —  We  have  seen  that 
in  the  quadrant  electrometer  it  is  necessary  to  give  the 
needle  a  high  initial  charge,  the   reason  being  that   if 
there  did  not  exist  between  the  quadrants  and  the  needle 
a  much  greater  difference  of  potential  than  the  small 
voltage  we  are  measuring,  the  force  tending  to  turn  the 
needle  would  be  too  small  to  be  conveniently  observed. 
Where,  however,  we  are  dealing  with  high  differences  of 
potential  a  separately-charged   needle  is  not   requisite ; 
we  may  simply  join  one  conductor   to  the  needle  and 
the    other   to    a   set   of    quadrants,    and    the    force   of 


276 


ELECTRICITY   AND   MAGNETISM      PART  n 


attraction,  which,  other  things  being  equal,  increases  as 
the  square  of  the  difference  of  potential,  is  sufficiently 
great  to  give  reliable  readings.  This 
is  known  as  the  idiostatic  method  of 
using  the  instrument. 

A  front  view  of  the  instrument  as 
commonly  used  to  measure  differences 
of  potential  of  1000  volts  or  more,  is 
shown  in  Fig.  153.  The  needle  NN 
is  a  paddle-shaped  plate  of  aluminium 
supported  by  knife  edges  at  its  centre ; 
its  position  is  controlled  by  gravity, 
little  weights  being  hung  on  a  projec- 
tion at  its  lower  end.  The  quadrants 
Q  are  both  behind  and  in  front  of  it, 
and  so  placed  that  when  a  difference 
of  potential  exists  between  the  needle  and  them  the 
needle  is  deflected  from  its  normal  position  and  moves 
its  pointer  over  a  graduated  scale. 

It  will  be  seen  that  it  does  not  matter  whether  the 
needle  is  positively  charged  and  the 
quadrants  negatively  charged  or  vice 
versa;  an  attraction  between  the  two 
will  always  take  place,  so  a  deflexion 
will  be  given  even  when  the  differ- 
ence of  potential  is  rapidly  alternat- 
ing. This  property  of  the  instrument 
makes  it  exceedingly  useful  for  the 
measurement  of  voltage  when  alter-, 
nating  currents  are  used. 

Another  advantage  of  this  instru- 
ment over  the  high-resistance  galva- 
nometers that  are  used  as  voltmeters  is, 
that  it  does  not  take  any  current,  and  con- 
sequently it  does  not  waste  any  power. 


Fig.  154. 


In  order  to  make  the  electrostatic  voltmeter  sufficiently 
delicate  to  measure  down  to  100  volts  or  so,  a  number  of 


CHAP,  iv        CAPACITY   OF   CONDENSERS  277 

needles  is  placed  horizontally  one  above  the  other  on 
a  vertical  aluminium  wire,  and  attracted  by  a  tier  of 
quadrants  symmetrically  placed  on  each  side ;  this  instru- 
ment is  Lord  Kelvin's  multicellular  voltmeter.  It  is  shown 
in  elevation  and  plan  in  Fig.  154. 

291.  Dry-Pile  Electrometer.  —  The  principle  of  sym- 
metry observed  in  the  Quadrant  Electrometer  was  pre- 
viously employed  in  the  Electroscope  of  Bohnenberger 
—  a  much  less  accurate  instrument  —  in  which  the  charge 
to  be  examined  was  imparted  to  a  single  gold  leaf,  placed 
symmetrically  between  the  poles  of  a  dry-pile  (Art.  193) 
toward  one  or  other  pole  of  which  the  leaf  was  attracted. 
Fechner  modified  the  instrument  by  connecting  the  + 
pole  of  the  dry-pile  with  a  gold  leaf  hanging  between 
two  metal  disks,  from  the  more  -f  of  which  it  was  re- 
pelled.    The  inconstancy  of  dry-piles  as  sources  of  electri- 
fication led  TIankel  to  substitute  a  battery  of  a  very  large 
number  of  small  Daniell's  cells. 

292.  Capillary  Electrometers.  —  The  Capillary  Elec- 
trometer of  Lippmann,  as  modified  by  Dewar,  was  de- 
scribed in  Art.  253. 


LESSON  XXIII.  —  Dielectric  Capacity,  etc. 

293.  A   Leyden    jar   or   other   condenser  may  be 
regarded  as  a  conductor,  in  which  (owing  to  the  particu- 
lar device  of  bringing  near  together  the  two  oppositely- 
charged  surfaces)  the  conducting  surface  can  be  made  to 
hold  a  very  large  charge  without  its  potential  (whether 
+  or  —  )  rising  very  high.     The  capacity  of  a  condenser, 
like  that  of  a  simple  conductor,  will  be  measured  (see 
Art.  271)  by  the  quantity  of  electricity  required  to  pro- 
duce unit  rise  of  potential. 

294.  Theory  of   Spherical   Condenser.  —  Suppose  a 
Leyden  jar  made  of  two  concentric  metal  spheres,  one 
inside  the  other,  the  space  between  them   being  filled 


278 


ELECTRICITY   AND   MAGNETISM      PART  n 


by  air. 


The  inner  one,  A,  will  represent  the  interior 
coating  of  tinfoil,  and  the 
outer  sphere,  B  (Fig.  155),  will 
represent  the  exterior  coating. 
Let  the  radii  of  these  spheres 
be  r  and  r1  respectively.  Sup- 
pose a  charge  of  Q  units  to  be 
imparted  to  A  ;  it  will  induce 
on  the  inner  side  of  B  an  equal 
negative  charge  —  Q,  and  to 
the  outer  side  of  B  a  charge 
+  Q  will  be  repelled.  This 
latter  is  removed  by  contact 
with  "  earth,"  and  need  be  no 
Fig.  155.  further  considered.  The  po- 

tential *  at  the  centre  M,  calculated  by  the  rule  given  in 

Art.  263,  will  be 


At  a  point  N,  outside  the  outer  sphere  and  quite  near  to 
it,  the  potential  will  be  the  same  as  if  these  two  charges, 
-f  Q  and  —  Q,  were  both  concentrated  at  M.  Hence 

,r  _  +  Q-Q 


r' 


=  0. 


So  then  the  difference  of  potentials  will  be 


whence 


Q 


rr' 


Q 


But  by  Art.  270  the  capacity  K  =        _       , 

*  M          *  N 

rr' 
therefore  K  =  -; 


*  The  student  must  remember  that  as  there  is  no  electric  force  within 
a  closed  conductor,  the  potential  at  the  middle  is  just  the  same  as  at  any 
other  point  inside. 


CEIAP.  iv  INDUCTIVITY  279 

We  see  from  this  formula  that  the  capacity  of  the 
condenser  is  proportional  to  the  size  of  the  metal  globes, 
and  that  if  the  insulating  layer  is  very  thin,  —  that  is,  if 
r  be  very  nearly  as  great  as  r',  r'  —  r  will  become  very 
small,  and  the  value  of  the  expression  -IL-  will  become 

very  great ;  which  proves  the  statement  that  the  capacity 
of  a  condenser  depends  upon  the  thinness  of  the  layer 
of  dielectric.  If  r'  is  very  great  compared  with  r,  the 
expression  for  the  capacity  becomes  equal  simply  to  r, 
that  of  the  inner  sphere  when  isolated. 

295.  Specific  Inductive  Capacity.  —  Cavendish  was 
the  first  to  discover  that  the  capacity  of  a  condenser 
depended  not  on  its  actual  dimensions  only,  but  upon  the 
inductive  power  of  the  material  used  as  the  dielectric  be- 
tween the  two  surfaces.  If  two  condensers  (of  any  of  the 
forms  to  be  described)  are  made  of  exactly  the  same  size, 
and  in  one  of  them  the  dielectric  be  a  layer  of  air,  and 
in  the  other  a  layer  of  some  other  insulating  substance, 
it  is  found  that  equal  quantities  of  electricity  imparted 
to  them  do  not  produce  equal  differences  of  potentials ; 
or,  in  other  words,  it  is  found  that  they  have  not  the 
same  capacity.  If  the  dielectric  be  mica,  for  example,  it 
is  found  that  the  capacity  is  about  six  times  as  great ;  for 
mica  possesses  a  high  inductive  power  and  allows  the 
transmission  across  it  of  electrostatic  influence  six  times 
as  well  as  air  does.  The  name  specific  inductive  capac- 
ity,* or  dielectric  capacity,  is  given  to  the  ratio  between 
the  capacities  of  two  condensers  equal  in  size,  one  of 
them  being  an  air  condenser,  the  other  filled  with  the 
specified  dielectric.  The  specific  inductive  capacity  of 
dry  air  at  the  temperature  0°  C.,  and  pressure  76  cen- 
timetres, is  taken  as  the  standard,  and,  in  the  absence  of 
any  known  way  of  finding  its  absolute  value,  is  reckoned 

*  The  name  is  not  a  very  happy  one, — inductivity  would  have  been 
better,  and  is  the  analogous  term,  for  dielectrics,  to  the  term  "conduc- 
tivity "  used  for  conductors.  The  term  dielectric  coefficient  is  also  used 
by  some  modern  writers. 


280 


ELECTRICITY   AND   MAGNETISM      PART  n 


as  unity.     The  symbol  k  is  used  to  denote  the  dielectric 
capacity  of  any  material. 

Cavendish,  about  the  year  1775,  measured  the  dielec- 
tric capacity  of  glass,  bees-wax,  and  other  substances,  by 
forming  them  into  condensers  between  two  circular  metal 
plates,  the  capacity  of  these  condensers  being  compared 
with  that  of  an  air  condenser  (resembling  Fig.  42)  and 
with  other  condensers  which  he 
called  "  trial-plates."  He  even 
went  so  far  as  to  compare  the 
capacities  of  these  "trial-plates" 
with  that  of  an  isolated  sphere 
of  12 1  inches  diameter  hung  up 
in  a  room. 

296.  Faraday's  Experi- 
ments. —  In  1837  Faraday,  who 
did  not  know  of  the  then 
unpublished  researches  of 
Cavendish,  independently  dis- 
covered specific  inductive  ca- 
pacity, and  measured  its  value 
for  several  substances,  using  for 
this  purpose  two  condensers  of 
the  form  shown  in  Fig.  156. 
Each  consisted  of  a  brass  ball  A, 
enclosed  inside  a  hollow  sphere 
of  brass  B,  and  insulated  by  a 
long  plug  of  shellac,  up  which 
passed  a  wire  terminating  in  a 
knob  a.  The  outer  sphere  con- 
sisted of  two  parts  which  could 


Fig.  156. 


be  separated  from  each  other  in  order  to  fill  the  hollow 
space  with  any  desired  material :  the  experimental  process 
then  was  to  compare  their  capacities  when  one  was 
filled  with  the  substance  to  be  examined,  the  other 
containing  only  dry  air.  One  of  the  condensers  was 
charged  with  electricity.  It  was  then  made  to  share  its 


CHAP,  iv  DIELECTRIC   CAPACITY  281 

charge  with  the  other  condenser,  by  putting  the  two  inner 
coatings  into  metallic  communication  with  one  another; 
the  outer  coatings  also  being  in  communication  with  one 
another.  If  their  capacities  were  equal  they  would  share 
the  charge  equally,  and  the  potential  after  contact  would 
be  just  half  what  it  was  in  the  charged  condenser  before 
contact.  If  the  capacity  of  one  was  greater  than  the 
other  the  final  potential  would  not  be  exactly  half  the 
original  potential,  because  they  would  not  share  the  charge 
equally,  but  in  proportion  to  their  capacities.  The  po- 
tentials of  the  charges  were  measured  before  and  after 
contact  by  means  of  a  torsion  balance.*  Faraday's  results 
showed  the  following  values  :  Sulphur,  2-26  ;  shellac,  2-0  ; 
glass,  1-76  or  more. 

297.  Recent  Researches.  —  Since  1870  large  addi- 
tions to  our  knowledge  of  this  subject  have  been  made. 
Gibson  and  Barclay  measured  the  inductivity  of  paraffin 
wax  by  comparing  the  capacity  of  an  air  condenser 
with  one  of  paraffin  by  means  of  an  arrangement  of  slid- 
ing condensers,  using  a  sensitive  quadrant  electrometer  to 
adjust  the  capacity  of  the  condensers  exactly  to  equality. 
Hopkinson  has  examined  the  dielectric  power  of  glass  of 
various  kinds,  using  a  constant  battery  to  produce  the 
required  difference  of  potentials,  and  a  condenser  provided 
with  a  guard-ring  for  a  purpose  similar  to  that  of  the 
guard-ring  in  absolute  electrometers.  Gordon  made  a 
large  number  of  observations,  using  a  delicate  apparatus 
known  as  a  statical  "inductivity  balance,"  which  is  a 
complicated  condenser,  so  arranged  in  connexion  with  a 

*  The  value  of  the  dielectric  capacity  k  could  then  be  calculated  as 
follows  :  — 


(where  K  is  the  capacity  of  the  first  apparatus  and  V  its  potential,  and 
V  the  potential  after  communication  with  the  second  apparatus,  whose 
capacity  is  Kk)  :  hence 


and 


282  ELECTRICITY  AND   MAGNETISM      PART  n 

quadrant  electrometer  that  when  the  capacities  of  the 
separate  parts  are  adjusted  to  equality  there  shall  be  no 
deflexion  in  the  electrometer,  whatever  be  the  amount  or 
sign  of  the  electrification  at  the  moment.  This  arrange- 
ment, when  employed  in  conjunction  with  an  induction 
coil  (Fig.  135)  and  a  rapid  commutator,  admits  of  the  in- 
ductive capacity  being  measured  when  the  duration  of 
the  actual  charge  is  only  very  small,  the  electrification 
being  reversed  12,000  times  per  second.  Such  an  instru- 
ment, therefore',  overcomes  one  great  difficulty  besetting 
these  measurements,  namely,  that  owing  to  the  apparent 
absorption  of  part  of  the  charge  by  the  dielectric  (as 
mentioned  in  Art.  61),  the  capacity  of  the  substance, 
when  measured  slowly,  is  different  from  its  "  instanta- 
neous capacity."  This  electric  absorption  is  discussed 
further  in  Art.  299.  For  this  reason  the  values  assigned 
by  different  observers  for  the  dielectric  capacity  of  various 
substances  differ  to  a  most  perplexing  degree,  especially 
in  the  case  of  the  less  perfect  insulators.  The  following 
table  summarizes  Gordon's  observations  :  — 

Air 1-00 

Glass 3-013    to  3' 258 

Ebonite 2'284 

Guttapercha         ....  2'462 

Indiarubber          ....  2'220   to  2 "497 

Paraffin  (solid)    .        ...  T9936 

Shellac 2'74 

Sulphur 2-58 

Hopkinson,  whose  method  was  a  "  slow "  one,  found 
for  glass  much  higher  inductive  capacities,  ranging  from 
6-5  to  10*1,  the  denser  kinds  having  higher  capacities. 
Mica  has  values  ranging  from  5-5  to  8.  Cavendish 
observed  that  the  apparent  capacity  of  glass  became  much 
greater  at  those  temperatures  at  which  it  begins  to  con- 
duct electricity.  Boltzmann  has  announced  that  in  the 
case  of  two  crystalline  substances,  Iceland  spar  and  sul- 
phur, the  inductive  capacity  is  different  in  different 


INDUCTIVITY   OF  FLUIDS 


283 


directions,  according  to  their  position  with  respect  to  the 
axes  of  crystallization. 

298.  Dielectric  Capacity  of  Liquids  and  Gases.  — 
The  dielectric  capacity  of  liquids  also  has  specific  values, 
as  follows :  — 


Turpentine 
Petroleum 
Bisulphide  of  Carbon 


2-16 

2-03  to  2-07 

1-81 


Faraday  examined  the  inductive  capacity  of  several 
gases  by  means  of  his  apparatus  (Fig.  156),  one  of  the 
condensers  being  filled  with  air,  the  other  with  the  gas 
which  was  let  in  through  the  tap  below  the  sphere  after 
exhaustion  by  an  air  pump.  The  method  was  too  rough, 
however,  to  enable  him  to  detect  any  difference  between 
them.  More  recently  Boltzrnann,  and  independently 
Ayrton  and  Perry,  have  measured  the  dielectric  capaci- 
ties of  different  gases  by  very  exact  methods ;  and  their 
results  agree  very  fairly. 


Boltzmann. 

Ayrton  and  Perry. 

Air       

(1) 

(1) 

Vacuum      .... 

(0-999410) 

(0-9985) 

Hydrogen    .... 

0-999674 

0-9998 

Carbonic  Acid     . 

1-000356 

1-0008 

Olefiant  Gas 

1-000722 

Sulphur  Dioxide 

1-0037 

The  effect  of  using  instead  of  air  a  medium  of  higher 
dielectric  power  k  is  to  change  the  forces  exerted  between 
charged  bodies.  For  given  fixed  charges  the  forces  vary 
inversely  as  k]  while  for  given  differences  of  potential 
between  the  bodies  the  forces  vary  directly  as  k. 

299.  Mechanical  Effects  of  Dielectric  Stress.  —  That 
different  insulating  substances  have  specific  inductive 
power  sufficiently  disproves  the  idea  that  influence  is 


284  ELECTRICITY   AND   MAGNETISM      PART  n 

merely  an  "  action  at  a  distance,"  for  it  is  evident  that 
the  dielectric  medium  is  itself  concerned  in  the  propaga- 
tion of  influence,  and  that  some  media  allow  influence  to 
take  place  across  them  better  than  others.  The  existence 
of  a  residual  charge  (Art.  61)  can  be  explained  either  on 
the  supposition  that  the  dielectric  is  composed  of  hetero- 
geneous particles  which  have  unequal  conducting  powers, 
as  Maxwell  has  suggested,  or  on  the  hypothesis  that  the 
molecules  are  actually  subjected  to  a  strain  from  which, 
especially  if  the  stress  be  long-continued,  they  do  not 
recover  all  at  once.  Kohlrausch  and  others  have  pointed 
out  the  analogy  between  this  phenomenon  and  that  of  the 
"  elastic  recovery"  of  solid  bodies  after  being  subjected  to 
a  bending  or  a  twisting  strain.  A  fibre  of  glass,  for 
example,  twisted  by  a  certain  force,  flies  back  when 
released  to  almost  its  original  position,  a  slight  sub-per- 
manent set  remains,  from  which,  however,  it  slowly 
recovers  itself,  the  rate  of  its  recovery  depending  upon 
the  amount  and  duration  of  the  original  twisting  strain. 
A  quartz  fibre  never  shows  any  sub-permanent  set.  Hop- 
kinson  has  shown  that  it  is  possible  to  superpose 
several  residual  charges,  even  charges  of  opposite  signs, 
which  apparently  "  soak  out  "as  the  strained  material 
gradually  recovers  itself.  Perry  and  Ayrton  have  also 
investigated  the  question,  and  have  shown  that  the 
polarization  charges  in  voltameters  exhibit  a  similar 
recovery.*  Air  condensers  exhibit  no  residual  charges. 
Nor  do  plates  of  quartz  cut  from  homogeneous  crystal. 
When  a  condenser  is  discharged  a  sound  is  often 
heard.  This  was  noticed  by  Lord  Kelvin  in  the  case 
of  air  condensers ;  Varley  and  Dolbear  have  constructed 
telephones  in  which  the  rapid  charge  and  discharge  of 

*  It  would  appear,  therefore,  probable  that  Maxwell's  suggestion  of 
heterogeneity  of  structure,  as  leading  to  residual  electrification  at  the 
bounding  surface  of  the  particles  whose  electric  conductivities  differ,  is  the 
true  explanation  of  the  "  residual "  charge.  The  phenomenon  of  elastic 
recovery  may  itself  be  due  to  heterogeneity  of  structure.  Glass  itself  is  a 
mixture  of  different  silicates. 


CHAP,  iv     POLARIZATION  OF   DIELECTRIC  285 

a  condenser  gave  rise  to  musical  tones  and  to  articulate 
speech. 

As  to  the  precise  nature  of  the  molecular  or  mechanical 
operations  in  the  dielectric  when  thus  subjected  to  the 
stress  of  electrostatic  induction,  nothing  is  known.  One 
pregnant  experiment  of  Faraday  is  of  great  importance, 
by  showing  that  induction  is,  as  he  expressed  it,  "  an 
action  of  contiguous  particles."  In  a  glass  trough  (Fig. 
157)  is  placed  some  oil  of  turpentine,  in  which  are  put 
some  fibres  of  dry 
silk  cut  into  small 
bits.  Two  wires 
pass  into  the 
liquid,  one  of 
which  is  joined 
to  earth,  the  other 

being  put  into  connexion  with  the  collector  of  an 
electrical  machine.  The  bits  of  silk  come  from  all  parts 
of  the  liquid  and  form  a  quivering  chain  of  particles  from 
wire  to  wire,  showing  the  electric  lines  of  force.  They 
at  once  disperse  if  the  electric  discharge  is  stopped. 
Faraday  regarded  this  as  typical  of  the  internal  actions 
in  every  case  of  influence  across  a  dielectric,  the  particles 
of  which  he  supposed  to  be  "polarized,"  that  is,  to  be 
turned  into  definite  positions,  each  particle  having  a 
positive  and  a  negative  end.  The  student  will  perceive 
an  obvious  analogy,  therefore,  between  the  condition  of 
the  particles  of  a  dielectric  across  which  influence  is 
taking  place,  and  the  molecules  of  a  piece  of  iron  or  steel 
when  subjected  to  magnetic  induction.  Instead  of  silk, 
crystals  of  sulphate  of  quinine  may  be  used.  Or  finely- 
divided  sulphide  of  antimony  may  be  strewn  on  the 
bottom  of  a  glass  dish  and  covered  with  a  layer  of 
petroleum,  to  show  the  electric  lines  of  force. 

Siemens  has  shown  that  the  glass  of  a  Leyden  jar 
is  sensibly  warmed  after  being  several  times  rapidly 
charged  and  discharged.  This  obviously  implies  that 


286  ELECTRICITY   AND   MAGNETISM      PART  n 


molecular  movement  accompanies  the  changes  of  dielec- 
tric stress. 

300.  Electric  Expansion.  —  Fontaua  noticed  that  the 
internal  volume  of  a  Leyden  jar  increased  when  it  was 
charged.     Priestly  and  Volta  sought  to  explain  this  by 
suggesting  that  the  attraction  between  the  two  charged 
surfaces  compressed  the  glass  and  caused  it  to  expand 
laterally.     Duter  showed  that  the  amount  of  apparent 
expansion  was  inversely  proportional  to  the  thickness  of 
the  glass,  and  varied  as  the  square  of  the  potential  differ- 
ence.     Quincke  has  recently  shown  that  though  glass 
and  some  other  insulators  exhibit  electrical  expansion, 
an   apparent  contraction   is  shown  by  resins   and  oily 
bodies  under  electrostatic  stress.    He  connects  with  these 
properties  the  production  of  optical  strain  and  of  double 
refraction  discovered  by  Kerr.     (See  Lesson  on  Electro- 
optics,  Art.  525). 

301.  Submarine    Cables    as    Condensers.  —  A    sub- 
marine telegraph   cable   may   act   as  a   condenser,   the 
ocean  forming  the  outer  coating,  the  internal  wire  the 
inner  coating,  while  the  insulating  layers  of  guttapercha 
serve  as  dielectric.     When  one  end  of  a  submerged  cable 
is  connected  to,  say,  the  +  pole  of  a  powerful  battery, 
electricity    flows    into    it.      Before    any    signal    can    be 
received  at  the  other  end,  enough  electricity  must  flow 
in  to  charge  the  cable  to  a  considerable  potential,  an 
operation  which  may  in  the  case  of  long  cables  require 
some  seconds.     Faraday  predicted  that  this  retardation 
would  occur.     It  is,  in  actual  fact,  a  serious   obstacle 
to  rapid  signalling  through  Atlantic  and  other  cables. 
Professor  Fleeming  Jenkin  has  given  the  following  ex- 
perimental demonstration  of  the  matter.     Let  a  mile  of 
insulated  cable  wire  be   coiled  up   in   a  tub  of  water 
(Fig.  158),  one  end  N  being  insulated.     The  other  end 
is  joined  up  through  a  long-coil  galvanometer  G  to  the 
+  pole  of  a  large  battery,  whose  —  pole  is  joined  by  a 
wire  to  the  water  in  the  tub.     Directly  this  is  done,  the 


CHAP.    IV 


CABLES   AS   CONDENSERS 


287 


needle  of  the  galvanometer  will  show  a  violent  deflexion, 
electricity  rushing  through  it  into  the  interior  of  the 
cable,  and  a  —  charge  being  accumulated  on  the  outside  of 
it  where  the  water  touches  the  guttapercha.  For  perhaps 
an  hour  the  flow  will  go  on,  though  diminishing,  until  the 
cable  is  fully  charged.  Now  remove  the  battery,  and 
instead  join  up  a  and  b  by  a  wire;  the  charge  in  the 
cable  will  rush  out  through  the  galvanometer,  which  will 


Fig.  158. 

show  an  opposite  deflexion,  and  the  residual  charge  will 
continue  "soaking  out"  for  a  long  time. 

Long  land-lines  carried  overhead  also  possess  a  measur- 
able capacity,  and  tend  to  retard  the  signals. 

3O2.  Use  of  Condensers.  —  To  obviate  this  retarda- 
tion and  increase  the  speed  of  signalling  in  cables  *  several 
devices  are  adopted.  Very  delicate  receiving  instruments 
are  used,  requiring  only  a  feeble  current;  for  with  the 
feebler  batteries  the  actual  charge  given  to  the  cable 
is  less.  In  some  cases  a  key  is  employed  which,  after 
every  signal,  immediately  sends  into  the  cable  a  charge 
of  opposite  sign,  to  sweep  out,  as  it  were,  the  charge  left 
behind.  Often  a  condenser  of  several  microfarads' 
capacity  is  interposed  in  the  circuit  at  each  end  of  the 
cable  to  curb  the  signal,  or  make  it  shorter  and  sharper, 
and  by  its  reaction  assist  the  discharge.  In  duplex 

*  The   capacity  of  the   "Direct"   Atlantic    cable    from   Ballinskelligs 
(Ireland)  to  Nova  Scotia  is  992  microfarads. 


ELECTRICITY   AND   MAGNETISM      PART  n 

signalling  (Art.  503)  the  resistance  and  electrostatic  capa- 
city of  the  cable  have  to  be  met  by  balancing  against 
them  an  "  artificial  cable  "  consisting  of  a  wire  of  equal 
resistance,  combined  with  a  condenser  of  equal  capacity. 
Messrs.  Muirhead  constructed  for  duplexing  the  Atlantic 
cable  a  condenser  containing  100,000  square  feet  (over 
two  acres  of  surface)  of  tinfoil.  Condensers  are  also 
occasionally  used  on  telegraph  lines  in  single  working  to 
obviate  disturbances  from  earth  currents.  They  are  con- 
structed by  placing  sheets  of  tinfoil  between  sheets  of 
mica  or  of  paraffined  paper,  alternate  sheets  of  foil  being 
connected  together.  The  paper  is  the  finest  bank-wove, 
carefully  selected  to  be  free  from  minute  holes.  Two 
thicknesses,  drawn  through  a  bath  of  the  purest  paraffin 
wax  heated  till  it  melts,  are  laid  between  each  foil  and 
the  next ;  care  being  taken  to  exclude  air  bubbles.  When 
a  sufficient  number  have  been  assembled  hot  they  are  put 
under  pressure  to  cool,  and  afterwards  adjusted.  Small 
condensers  of  similar  construction  are  used  in  connexion 
with  induction  coils  (Fig.  135). 

3O3.  Practical  Unit  of  Capacity.  —  Electricians  adopt 
a  unit  of  capacity,  termed  one  farad,  based  on  the  system 
of  electromagnetic  units.  A  condenser  of  one  farad 
capacity  would  be  raised  to  a  po- 
tential of  one  volt  by  a  charge  of 
one  coulomb  of  electricity.*  In 
practice  such  a  condenser  would  be 
too  enormous  to  be  constructed; 
the  earth  itself,  as  an  isolated 
sphere,  has  a  capacity  of  only 
Ttfiysu  °^  a  fara(i.  As  a  practical 
unit  of  capacity  is  therefore  chosen 
the  microfarad,  or  one  millionth 

of  a  farad ;  a  capacity  about  equal  to  that  of  three  miles 
of  an  Atlantic  cable.  Condensers  of  only  |  microfarad 
capacity  are  about  equal  to  one  nautical  mile  of  cable. 
They  contain  about  1200  square  inches  of  foil.  The 

*  See  list  of  Practical  Electromagnetic  Units,  Art.  354. 


CHAP,  iv       CALCULATION  OF  CAPACITY  289 

dielectric  in  them  is  usually  mica,  in  thin  sheets.  Their 
general  form  is  shown  in  Fig.  159.  The  two  brass  pieces 
upon  the  ebonite  top  are  connected  respectively  with  the 
two  series  of  alternate  sheets  of  tinfoil.  The  plug  between 
them  serves  to  keep  the  condenser  discharged  when  not 
in  use. 

Methods  of  measuring  the  capacity  of  a  condenser 
are  given  in  Art.  418. 

304.  Formulae  for  Capacities  of  Conductors  and 
Condensers.  —  The  following  formulae  give  the  capacity 
of  condensers  of  all  ordinary  forms,  in  electrostatic 
units  :  — 

Sphere:  (radius  =  r.     See  Art.  271). 

K  =  r. 

Ttco  Concentric  Spheres:  (radii  r  and  r',  dielectric 
capacity,  k). 

K  =  k  -^—- 
r  —  r 

Cylinder:  (length  =  /,  radius  =  r). 
I 


2logel- 


Two    Concentric   Cylinders:    (length  =  I,   dielectric 
capacity  =  k,  internal  radius  =  r,  external  radius 


2loger- 

Circular  Disk:  (radius  =  r,  thickness  negligible). 

K  =  2r/7r. 
Two  Circular  Disks:  (like  air  condenser,  Art.  56, 

radii  =  r,  surface  =  S,  thickness  of  dielectric  =  b, 

dielectric  capacity  =  &)  . 


or 


200  ELECTRICITY   AND   MAGNETISM      PART  n 


The  latter  formula  applies  to  any  two  parallel  disks 
of  surface  S,  whether  circular  or  otherwise,  provided  they 
are  large  as  compared  with  the  distance  b  between  them. 
To  calculate  down  to  microfarads  the  numbers  given  by 
any  of  the  above  must  be  divided  by  900,000. 

305.  Energy  of    Discharge    of    Ley  den  Jar  or  Con- 
denser. —  It   follows   from   the    definition   of    potential, 
given   in    Art.  263,  that  in  bringing  up  one   +  unit  of 
electricity  to  the  potential  V,  the  work  done  is  V  ergs. 
This  assumes,  however,  that  the  total  potential  V  is  not 
thereby  raised,  and  on  this  assumption  the  work*  done 
in  bringing  up  Q  units  would  be  QV  ergs.     If,  however, 
the  potential  is  nothing  to  begin  with,  and  is  raised  to  V 
by  the  charge  Q,  the  average  potential  during  the  opera- 
tion is  only  £V ;  hence  the  total  work  done  in  bringing  up 
the  charge  Q  from  zero  potential  to  potential  V  is  ^QV 
ergs.     Now,  according  to  the  principle  of  the  conservation 
of  energy,  the  work  done  in  charging  a  jar  or  condenser 
with  electricity  is  equal  to  the  work  which  could  be  done 
by  that  quantity  of  electricity  when  the  jar  is  discharged. 
Hence  |QV  represents  also  the  energy  of  the  discharge. 

Since  Q  =  VK,  it  follows  that  we  may  write  ]QV  in 

02 
the  form  JJS-.    That  is  to  say,  if  a  condenser  of  capacity  K 

is  charged  by  having  a  charge  Q  imparted  to  it,  the  energy 
of  the  charge  is  proportional  directly  to  the  square  of  the 
quantity,  and  inversely  to  the  capacity  of  the  condenser. 

306.  Symbol  for   Condenser.  —  Electricians  use   as 
symbols  for  condensers  in  diagrams  of  electric  circuits 

those  given  in  Fig.  160. 
The  origin  of  these 
symbols  is  the  alternate 
layers  of  tinfoils.  The 
symbol  on  the  right 
suggests  six  layers  of  foil,  of  which  the  first,  third,  and 

*  If  Q  is  given  in  coulombs  and  V  in  volts,  the  work  will  be  expressed 
not  in  ergs  but  in  joules  (Art.  354). 


CHAP,  iv         CAPACITIES   IN   PARALLEL  291 

fifth  are  joined   together,  and  the  second,  fourth,  and 
sixth  are  also  joined  together. 

307.  Capacities  joined  in  Parallel.  —  To  join  two 
condensers  together  in  parallel  the  positive  foils  of  one 
are  joined  to  the  positive  foils  of  the  other,  and  their 
negative  foils  are  also  joined  together.  In  Fig.  161  the 
two  condensers  Kx  and  K2  are  joined  in  parallel.  They 
will  thus  act  simply  like  one  large  condenser  of  capacity 
—  Kj  +  K2.  Any  charge  flowing  in  on  the  -f  side  will 
divide  between  the  twro  in  proportion  to  their  capacities. 

If  two  equal  Leyden  jars  are  charged  to  the  same 
potential,  and  then  their  inside  and  outside  coatings  are 
respectively  joined,  their 
united  charge  will  be  the 
same  as  that  of  a  jar  of 
equal  thickness,  but  hav- 
ing twice  the  amount  of 
surface. 

If  a  charged  Leyden 
jar  is  placed  similarly  in 
communication  with  an  uncharged  jar  of  equal  capacity, 
the  charge  will  be  shared  equally  between  the  two  jars, 
and  the  passage  of  electricity  from  one  to  the  other  will  be 
evidenced  by  the  production  of  a  spark  when  the  respective 
coatings  are  put  into  communication.  Here,  however,  half 
the  energy  of  the  charge  is  lost  in  the  operation  of  sharing 
the  charge,  for  each  jar  will  have  only  £Q  for  its  charge 
and  JV  for  its  potential ;  hence  the  energy  of  the  charge 
of  each,  being  half  the  product  of  charge  and  potential,  will 
only  be  one  quarter  of  the  original  energy.  The  spark 
which  passes  in  the  operation  of  dividing  the  charge  is, 
indeed,  evidence  of  the  loss  of  energy ;  it  is  about  half  as 
powerful  as  the  spark  would  have  been  if  the  first  jar  had 
been  simply  discharged,  and  it  is  just  twice  as  powerful 
as  the  small  sparks  yielded  finally  by  the  discharge  of 
each  jar  after  the  charge  has  been  shared  between  them. 

The  energy  of  a  charge  of  the  jar  manifests  itself,  as 


292  ELECTRICITY   AND   MAGNETISM      PART  n 

stated  above,  by  the  production  of  a  spark  at  discharge  ; 
the  sound,  light,  and  heat  produced  being  the  equivalent 
of  the  energy  stored  up.  If  discharge  is  effected  slowly 
through  a  long  thin  wire  of  high  resistance  the  air  spark 
may  be  feeble,  but  the  wire  may  be  perceptibly  heated. 
A  wet  string  being  a  feeble  conductor  affords  a  slow  and 
almost  silent  discharge;  here  probably  the  electrolytic 
conduction  of  the  moisture  is  accompanied  by  an  action 
resembling  that  of  secondary  batteries  (Lesson  492)  tend- 
ing to  prolong  the  duration  of  the  discharge. 

308.  Capacities  joined  in  Series.  —  If  two  condensers 
are  joined  in  series  they  will  act  as  a  condenser  having  a 
lesser  capacity  than  either  of  them  separately.  Their 
joint  capacity  in  series  icill  be  the  reciprocal  of  the  sum  of  the 
reciprocals  of  their  capacities  separately. 

Proof.  —  Let  two  condensers  K!  and  K.2  be  set  in  series  (Fig. 

102)  between  two  points  across  which  there  is  a  difference  of 
potential  V.  This  difference  of 
potential  will  be  divided  between 
the  two  inversely  in  proportion 
to  their  capacities,  seeing  that 
the  quantities  of  electricity  that 
are  displaced  into  and  out  of 
their  respective  coatings  are  nec- 
essarily equal.  Or,  if  Q  be  this 

quantity,  and  K3  the  effective  or  joint  capacity  of  the  two 

together,  to  find  the  latter,  we  have  :  — 

Q  =  V^  =  V2K2  -  VK8       ...        (1) 
and          V=Vi  +  V2  ......        (2) 

From  (1)  we  get 

V^VKs/Ki, 
and 

V2  =  VK3/K2. 

Inserting  these  in  (2)  we  get 


whence,  dividing  down  by  VK3,  we  get 

JL*i  +  JL  .  ,         .  .  Q.E.D. 

K3       KI       K2 


CHAP,  iv       PHENOMENA   OF   DISCHARGE  293 


Example.  — If  two  condensers,  respectively  3  and  2  microfarads,  are 
joined  in  series,  they  will  act  as  a  single  condenser  of  capacity 
'=  1  / (s  +  5)  =  1  E  microfarads. 

309.  Charge  of  Jars  arranged  in  Cascade.  —  Frank- 
lin suggested  that  a  series  of  jars  might  be  arranged, 
the  outer  coating  of  one  being  connected  with  the  inner 
one  of  the  next,  the  outer  coating  of  the  last  being  con- 
nected to  earth.  The  object  of  this  arrangement  was  that 
the  second  jar  might  be  charged  with  the  electricity 
repelled  from  the  outer  coating  of  the  first,  the  third  from 
that  of  the  second,  and  so  on.  This  "  cascade  "  arrange- 
ment, however,  is  of  no  advantage,  the  sum  of  the 
charges  accumulated  in  the  series  being  only  equal  to  that 
of  one  single  jar  if  used  alone.  For  if  the  inner  coating 
of  the  first  jar  be  raised  to  V,  that  of  the  outer  coating  of 
the  last  jar  remaining  at  zero  in  contact  with  earth,  the 
difference  of  potential  between  the  outer  and  inner  coat- 
ing of  any  one  jar  will  be  only  _V,  where  n  is  number  of 

n    . 

jars.     And   as  the   charge   in   each   jar  is  equal  to  its 
capacity  K,   multiplied  by  its  potential,  the  charge  in 

each  will  only  be  -  KV,  and  in  the  whole  n  jars  the  total 

n 

charge  will  be  n-KV,  or  KV,  or  equals  the  charge  of  one 
jar  of  capacity  K  raised  to  the  same  potential  V. 


LESSON  XXIV.  —  Phenomena  of  Discharge 

310.  Conductive  Discharge.  —  An  electrified  conduc- 
tor may  be  discharged  in  at  least  three  different  ways, 
depending  on  the  medium  through  which  the  discharge 
is  effected,  and  varying  with  the  circumstances  of  the  dis- 
charge. If  the  discharge  takes  place  by  the  passage  of 
a  continuous  current,  as  when  electricity  flows  through 
a  thin  wire  connecting  the  knobs  of  an  influence  machine, 
or  joining  the  positive  pole  of  a  battery  to  the  negative 


294  ELECTRICITY   AND    MAGNETISM      PART  11 

pole,  the  operation  is  termed  a  "  conductive  "  discharge. 
Under  some  circumstances  a  conductive  discharge  takes 
the  nature  of  an  oscillation  to  and  fro  (Art.  515). 

311.  Disruptive  Discharge.  —  It  has  been  shown 
how  influence  across  a  non-conducting  medium  is  always 
accompanied  by  a  mechanical  stress  upon  the  medium ; 
the  tension  along  the  electric  lines  of  force  increasing  as 
the  square  of  the  intensity  of  the  electric  field.  If  this 
stress  is  very  great  the  non-conducting  medium  will 
suddenly  give  way  and  a  spark  will  burst  across  it. 
Such  a  discharge  is  called  a  "  disruptive  "  discharge. 

A  very  simple  experiment  will  set  the  matter  in  a 
clear  light.  Suppose  a  metal  ball  charged  with  +  elec- 
trification to  be  hung  by  a  silk  string  above  a  metal  plate 
lying  on  the  ground.  If  we  lower  down  the  suspended 
ball  a  spark  will  pass  between  it  and  the  plate  when  they 
come  very  near  together,  and  the  ball  will  then  be  found 
to  have  lost  all  its  previous  charge.  It  was  charged  with 
a  certain  quantity  of  electricity ;  and  as  it  had,  when 
suspended  out  of  the  range  of  other  conductors,  a  certain 
capacity  (numerically  equal  to  its  radius  in  centimetres), 
the  electricity  on  it  would  be  at  a  certain  potential 
(namely  =  Q/K)>  arjd  the  charge  would  be  distributed 
uniformly  all  over  it.  The  plate  lying  on  the  earth 
would  be  all  the  while  at  zero  potential.  But  when  the 
suspended  ball  was  lowered  down  towards  the  plate  the 
previous  state  of  things  was  altered.  In  the  presence  of 
the  4-  charge  of  the  ball  the  potential*  of  the  plate 
would  rise,  were  it  not  that,  by  influence,  just  enough 
negative  electrification  appears  on  it  to  keep  its  potential 
still  the  same  as  that  of  the  earth.  The  tension  in  the 
electric  field  will  draw  the  +  charge  of  the  ball  down- 
wards, and  alter  the  distribution  of  the  charge,  the  surface- 
density  becoming  greater  at  the  under  surface  of  the  ball 

*  The  student  must  remember  that,  by  the  definition  of  potential  in 
Art.  2C3,  the  potential  at  a  point  is  the  sum  of  all  the  separate  quantities  of 
electricity  noar  it,  divided  each  by  its  distance  from  the  point. 


CHAP,  iv  LENGTH  OF  SPAttlv  295 

and  less  on  the  upper.  The  capacity  of  the  ball  will  be 
increased,  and  therefore  its  potential  will  fall  corre- 
spondingly. The  layer  of  air  between  the  ball  and  the 
plate  is  acting  like  the  glass  of  a  Ley  den  jar.  The  more 
the  ball  is  lowered  down  the  greater  is  the  accumulation 
of  the  opposite  kinds  of  charge  on  each  side  of  the  layer 
of  air,  and  the  tension  across  the  layer  becomes  greater 
and  greater,  until  the  limit  of  the  dielectric  strength  is 
reached ;  the  air  suddenly  gives  way  and  the  spark  tears 
a  path  across. 

312.  Convective  Discharge.  —  A  third  kind  of  dis- 
charge, differing  from  either  of  those  above  mentioned, 
may  take  place,  and  occurs  chiefly  when  electricity  of  a 
high  potential  discharges  itself  at  a  pointed  conductor  by 
accumulating  there  with  so  great  a  density  as  to  electrify 
the  neighbouring  particles  of  air;  these  particles   then 
flying  off  by  repulsion,  conveying  away  part  of  the  charge 
with  them.      Such  convective  discharges  may  occur  either 
in  gases  or  in  liquids,  but  are  best  manifested  in  air  and 
other  gases  at  a  low  pressure,  in  tubes  exhausted  by  an 
air  pump. 

The  discharge  of  a  quantity  of  electricity  in  any  of  the 
above  ways  is  always  accompanied  by  a  transformation  of 
its  energy  into  energy  of  some  other  kind,  —  sound,  light, 
heat,  chemical  actions,  and  other  phenomena  being  pro- 
duced. These  effects  must  be  treated  in  detail. 

313.  Length   of   Spark.  —  Generally   speaking,   the 
length  of  spark  between  two  conductors  increases  with 
the  difference  between  their  potentials.     It  is  also  found 
to  increase  when  the  pressure  of  the  air  is  diminished. 
Riess  found  the  distance  to  increase  in  a  proportion  a 
little  exceeding  that  of  the  difference  of  potentials.   Lord 
Kelvin   confirmed  this  by  measuring  by  means  of  an 
"absolute  electrometer"    (Art.   287)  the   difference   of 
potential  necessary  to  produce  a  spark  discharge  between 
two  parallel  plates  at  different  distances.      De  la  Rue 
and  Miiller  found  with  their  great  battery  (Art.  186) 


296  ELECTRICITY   AND   MAGNETISM      PART  n 

that  with  a  difference  of  potential  of  1000  volts  the  strik- 
ing distance  of  the  spark  was  only  -0127  centimetres  (or 
about  ^JQ  of  an  inch),  and  with  a  difference  of  10,000 
volts  only  1-369.  Their  11,000  silver  cells  gave  a  spark 
of  1-59  centim.  (about  f-  of  an  inch)  long.  To  produce  a 
spark  one  mile  long,  through  air  at  the  ordinary  pressure, 
would  therefore  require  a  difference  of  potential  exceed- 
ing that  furnished  by  1,000,000,000  Daniell's  cells  ! 

The  length  of  the  spark  differs  in  different  gases, 
being  nearly  twice  as  long  in  hydrogen  as  in  air  at  the 
same  density.  Or  to  produce  in  hydrogen  a  spark  as 
long  as  one  in  air  requires  less  voltage.  On  the  other 
hand,  carbonic  acid  gas,  whilst  it  is  stronger  than  air  for 
short  sparks,  is  weaker  for  long  ones. 

The  potential  needful  to  produce  a  spark  of  given 
length  in  a  given  gas  is  independent  of  the  kind  of  metal 
used  as  electrodes,  but  depends  upon  their  shape.  If 
points  are  used  instead  of  balls  it  is  found  that  at  equal 
voltage,  points  are  best  for  long  sparks,  but  are  worst  for 
short  sparks. 

According  to  Peace's  observations  a  minimum  poten- 
tial of  between  300  and  400  volts  is  necessary  to  start  a 
spark,  however  short,  in  air.  For  sparks  not  under  two 
millimetres  in  length  the  volts  necessary  to  start  a  spark 
across  a  length  of  I  centimetres  may  be  approximately 
expressed  by  the  equation  — 

V=  1500  +  30,000  Z. 

The  following  table,  calculated  from  the  results  of 
Heydweiller,  gives  the  volts  necessary  to  produce  a  spark 
in  air  at  15°  C.  and  76  centimetres  pressure  between  two 
spheres  of  various  sizes.  The  figures  must  be  increased  1 
per  cent  for  a  fall  of  3  degrees  of  temperature,  or  for  a 
rise  of  8  millimetres  of  pressure. 


CHAP.    IV 


LENGTH   OF   SPARK 


297 


Radius  of  Balls. 

Distance  between  Balls  (Centims.). 

o-i 

0-5 

1-0 

1-5 

Centims. 
2-5 

Volts. 
4500 

Volts. 
18900 

Volts. 
33840 

Volts. 
47610 

1-0 

4860 

18030 

32120 

411(50 

0-5 

4950 

17790 

27810 

32400 

0-25 

4980 

16200 

20790 

22980 

In  rarefied  air  the  spark  is  longer.  Snow  Harris 
stated  that  the  length  of  spark  was  inversely  propor- 
tional to  the  pressure,  but  this  law  is  not  quite  correct, 
being  approximately  true  only  for  pressures  between 
that  of  11  inches  of  mercury  and  that  of  30  inches  (one 
atmosphere).  At  lower  pressures,  as  Gordon  found,  a 
greater  difference  of  potential  must  be  used  to  produce 
a  spark  than  that  which  would  accord  with  Harris's  law. 
From  this  it  would  appear  that  thin  layers  of  air  oppose 
a  proportionally  greater  resistance  to  the  piercing  power 
of  the  spark  than  thick  layers,  and  possess  greater  dielec- 
tric strength. 

Faraday,  using  two  spheres  of  different  sizes,  found 
the  spark-length  greater  when  the  smaller  sphere  was 
positive  than  when  it  was  negative. 

With  rapidly  alternating  differences  of  potential, 
smaller  virtual  voltages  suffice  for  the  same  spark-length, 
for  the  length  depends  on  the  maximum,  not  on  the 
mean  value.  Using  a  ball  of  1  cm.  diameter  and  a  disk, 
Alexander  Siemens  found  3200  virtual  volts  to  be  needed 
at  0-1  cm.  distance,  and  11,000  at  0-5  cm.  distance  apart. 

The  dielectric  strength  of  a  gas  appears  to  be  weaker 
when  field  is  varying  than  when  it  is  steady.  When  the 


298  ELECTRICITY  AND   MAGNETISM      PART  n 

voltage  is  nearly  high  enough  to  produce  a  spark,  revers- 
ing the  poles  will  sometimes  start  a  spark.  Moreover, 
when  once  a  spark  has  passed  it  is  easier  for  a  second  one 
to  follow  on  the  same  track.  Probably  the  first  spark 
produces  chemical  dissociations  in  its  path  which  do  not 
instantly  pass  away. 

Hertz  made  the  singular  observation  that  ultra-violet 
light  (i.e.  actinic  waves)  falling  upon  the  kathode  surface 
assist  it  to  discharge  (see  Art.  351). 

A  perfect  vacuum  is  a  perfect  insulator  —  no  spark 
will  cross  it.  It  is  possible  to  exhaust  a  tube  so  perfectly 
that  none  of  our  electric  machines  or  appliances  can  send 
a  spark  through  the  vacuous  space  even  over  so  short  a 
distance  as  one  centimetre. 

On  the  other  hand,  a  great  increase  of  pressure  also 
increases  the  dielectric  strength  of  air,  and  causes  it  to 
resist  the  passage  of  a  spark.  Cailletet  compressed  dry 
air  at  40  to  50  atmospheres'  pressure,  and  found  that 
even  the  spark  of  a  powerful  induction  coil  failed  to 
cross  a  space  of  -05  centimetres'  width. 

314.  Flames  and  Hot  Air.  —  The  arc  produced  by 
the  passage  of  an  electric  current  between  two  carbon 
poles  is  treated  of  in  Art.  448.  It  is  a  species  of  flame 
which  conducts  the  current  from  the  tip  of  one  carbon 
rod  to  the  other,  while  volatilizing  the  carbon,  and  requires 
only  some  thirty  to  fifty  volts  for  its  maintenance.  The 
alternate-current  arc  generated  in  air  by  high-frequency 
discharges  at  a  potential  of  10,000  to  50,000  volts  is  a 
different  phenomenon,  and  is  apparently  an  endothermic 
flame  of  nitrogen  and  oxygen  burned  together. 

Sparks  are  longer  and  straighter  through  hot  air 
than  through  cold.  If  air  or  other  permanent  gas  is, 
however,  heated  in  a  closed  vessel  so  that  its  density 
remains  unaltered,  the  voltage  needful  to  produce  dis- 
charge remains  the  same ;  unless,  indeed,  the  gas  be 
heated  to  point  of  dissociation  when  discharge  occurs  at 
low  voltage. 


CHAP,  iv  PROPERTIES   OF   FLAME  299 

Flames  and  currents  of  very  hot  air,  such  as  those 
rising  from  a  red-hot  piece  of  iron,  are  extremely  good 
conductors  of  electricity,  and  act  even  better  than 
metallic  points  in  discharging  a  charged  conductor. 
Gilbert  showed  that  an  electrified  body  placed  near  a 
flame  lost  its  charge ;  and  the  very  readiest  way  to  rid 
the  surface  of  a  charged  body  of  low  conducting  power  of 
a  charge  imparted  to  it  by  friction  or  otherwise,  is  to  pass 
it  through  the  flame  of  a  spirit-lamp.  Faraday  found 
negative  electrification  to  be  thus  more  easily  discharged 
than  positive.  Flames  powerfully  negatively  electrified 
are  repelled  from  conductors,  though  not  so  when  posi- 
tively electrified.  Sir  W.  Grove  showed  that  a  current 
is  set  up  in  a  platinum  wire,  one  end  of  which  touches 
the  tip,  and  the  other  the  base,  of  a  flame. 

Guthrie  showed  that  a  red-hot  iron  ball  cannot  be 
positively,  but  may  be  negatively  charged.  When  white- 
hot  it  will  retain  neither  kind  of  charge. 

315.  Mechanical  Effects.- — Chief  amongst  the  me- 
chanical effects  of  the  disruptive  spark  discharge  is  the 
shattering  and  piercing  of  glass  and  other  insulators. 
The  dielectric  strength  of  glass,  though  much  greater 
than  that  of  air,  is  not  infinitely  great.  A  slab  of  glass 
3  inches  thick  has  been  pierced  by  the  discharge  of  a 
powerful  induction  coil.  The  so-called  "  toughened " 
glass  has  a  greater  dielectric  strength  than  ordinary  glass, 
and  is 'more  difficult  to  pierce.  A  sheet  of  glass  may  be 
readily  pierced  by  a  spark  from  a  large  Ley  den  jar  or 
battery  of  jars,  by  taking  the  following  precautions:  — 
The  glass  to  be  pierced  is  laid  upon  a  block  of  glass  or 
resin,  through  which  a  wire  is  led  by  a  suitable  hole,  one 
end  of  the  wire  being  connected  with  the  outer  coating 
of  the  jar,  the  other  being  cut  off  flush  with  the  surface. 
Upon  the  upper  surface  of  the  sheet  of  glass  that  is  to  be 
pierced  another  wire  is  fixed  upright,  its  end  being  exactly 
opposite  the  lower  wire,  the  other  extremity  of  this  wire 
being  armed  with  a  metal  knob  to  receive  the  spark  from 


300  ELECTRICITY   AND   MAGNETISM      PART  n 

the  knob  of  the  jar  or  discharger.  To  ensure  good  insula- 
tion a  few  drops  of  paraffin  oil,  or  of  olive  oil,  are  placed 
upon  the  glass  round  the  points  where  the  wires  touch  it. 
A  piece  of  dry  wood  similarly  treated  is  split  by  a  power- 
ful spark.  A  layer  of  oil  resists  being  pierced  as  much 
as  a  layer  of  air  five  or  six  times  as  thick  would  do. 

If  a  spark  is  led  through  a  tightly-corked  glass  tube 
containing  water,  the  tube  will  be  shattered  into  small 
pointed  fragments  by  the  sudden  expansion  of  the  liquid. 

Lullin  observed  two  curious  effects  when  a  piece  of 
cardboard  is  perforated  by  a"  spark  between  two  metal 
points.  Firstly,  there  is  a  slight  burr  raised  on  each  side, 
as  if  the  hole  had  been  pierced  from  the  middle  outwards, 
as  though  the  stress  in  the  air  had  pulled  at  the  card. 
Secondly,  if  the  two  points  are  not  exactly  opposite  one 
another  the  hole  is  found  to  be  nearer  the  negative  point. 
But  if  the  experiment  is  tried  under  the  air  pump  in  a 
vacuum,  there  is  no  such  displacement  of  the  hole ; .  it  is 
then  midway  exactly. 

The  mechanical  action  of  the  brush  discharge  at 
points  is  mentioned  in  Art.  47,  and  the  mechanical 
effects  of  a  current  of  electricity  were  described  in 
Lesson  XVI. 

316.  Chemical  Effects.  —  The  chemical  actions  pro- 
duced by  currents  of  electricity  have  been  described  in 
Lessons  XIV.  and  XIX.  Similar  actions  can  be  produced 
by  the  electric  spark,  and  by  the  silent  glow  discharge 
(see  Art.  319).  Faraday  showed,  indeed,  that  electricity 
from  all  kinds  of  different  sources  produced  the  same 
kinds  of  chemical  actions,  and  he  relied  upon  this  as  one 
proof  of  the  essential  identity  of  the  electricity  produced 
in  different  ways.  If  sparks  from  an  electric  machine  are 
received  upon  a  piece  of  white  blotting-paper  moistened 
with  a  solution  of  iodide  of  potassium,  brown  patches  are 
noticed  where  the  spark  has  effected  a  chemical  decom- 
position and  liberated  the  iodine. 

When  a  stream  of  sparks  is  passed  through  moist  air 


CHAP,  iv     CHEMICAL  ACTION  OF   SPARKS  301 

in  a  vessel,  the  air  is  found  to  have  acquired  the  property 
of  changing  to  a  red  colour  a  piece  of  paper  stained  blue 
with  litmus.  This,  Cavendish  showed,  was  due  to  the 
presence  of  nitric  acid,  produced  by  the  chemical  union 
of  the  nitrogen  and  oxygen  of  the  air.  The  effect  is  best 
shown  with  the  stream  of  sparks  yielded  by  a  small  in- 
duction coil  (Fig.  135),  in  a  vessel  in  which  the  air  has 
been  compressed  beyond  the  usual  atmospheric  pressure. 

Whenever  an  electric  machine  is  giving  out  high-volt- 
age discharges  a  peculiar  odour  is  perceived.  This  was 
formerly  thought  to  be  evidence  of  the  existence  of  an 
electric  "effluvium"  or  fluid;  it  is  now  known  to  be 
due  to  the  presence  of  ozone,  a  modified  form  of  oxygen 
gas,  which  differs  from  oxygen  in  being  denser,  more 
active  chemically,  and  in  having  a  characteristic  smell. 
The  silent  discharge  of  the  influence  machine  and  that  of 
the  induction  coil  are  particularly  favourable  to  the  pro- 
duction of  this  substance. 

The  spark  will  decompose  ammonia  gas,  and  olefiant 
gas,  and  it  will  also  cause  chemical  combination  to  take 
place  with  explosion,  when  passed  through  detonating 
mixtures  of  gases.  Thus  equal  volumes  of  chlorine  and 
hydrogen  are  exploded  by  the  spark.  So  are  oxygen  and 
hydrogen  gases,  when  mixed  in  the  proportion  of  two 
volumes  of  the  latter  to  one  of  the  former.  Even  the 
explosive  mixture  of  common  coal  gas  mixed  with  from 
four  to  ten  times  its  own  volume  of  common  air,  can  be 
thus  detonated.  A  common  experiment  with  the  so-called 
electric  pistol  consists  in  tilling  a  small  brass  vessel  with 
detonating  gases  and  then  exploding  them  by  a  spark. 
The  spark  discharge  is  sometimes  applied  to  the  firing  of 
blasts  and  mines  in  military  operations. 

317.  Heating  Effects.  —  The  flow  of  electricity 
through  a  resisting  medium  is  in  every  case  accompanied 
by  an  evolution  of  heat.  The  laws  of  heating  due  to 
currents  are  given  in  Art.  427.  The  disruptive  discharge 
is  a  transfer  of  electricity  through  a  medium  of  great  re- 


302  ELECTRICITY   AND   MAGNETISM      PART  n 

sistance  and  accompanied  by  an  evolution  of  heat.  A  few 
drops  of  ether  in  a  metallic  spoon  are  easily  kindled  by 
an  electric  spark.  The  spark  from  an  electric  machine, 
or  even  from  a  rubbed  glass  rod,  suffices  to  kindle  an 
ordinary  gas-jet.  In  certain  districts  of  America,  during 
the  driest  season  of  the  year,  the  mere  rubbing  of  a  per- 
son's shoes  against  the  carpet,  as  he  shuffles  across  the 
floor,  generates  sufficient  electrification  to  enable  sparks 
to  be  drawn  from  his  body,  and  he  may  light  the  gas  by 
a  single  spark  from  his  outstretched  finger.  Gunpowder 
can  be  fired  by  the  discharge  of  a  Leyden  jar,  but  the 
spark  should  be  retarded  by  being  passed  through  a  wet 
thread,  otherwise  the  powder  will  simply  be  scattered  by 
the  spark. 

The  Electric  Air-Thermometer,  invented  by  Kinnersley,* 
serves  to  investigate  the  heating  powers  of  the  discharge. 
It  consists  of  a  glass  vessel  enclosing  air,  and  communi- 
cating with  a  tube  partly  filled  with  water  or  other  liquid 
in  order  to  observe  changes  of  volume  or  of  pressure. 
Into  this  vessel  are  led  two  metal  rods,  between  which  is 
suspended  a  thin  wire,  or  a  filament  of  gilt  paper;  or  a 
spark  can  be  allowed  simply  to  cross  between  them. 
When  the  discharge  passes  the  enclosed  air  is  heated, 
expands,  and  causes  a  movement  of  the  indicating  column 
of  liquid.  The  results  of  observation  with  these  instru- 
ments are  as  follows  :  —  The  heating  effect  produced  by  a 
given  charge  in  a  wire  of  given  length  is  inversely 
proportional  to  the  square-of  the  area  of  the  cross  section 
of  the  wire.  The  total  heat  evolved  is  jointly  propor- 
tional to  the  charge,  and  to  the  potential  through  which 
it  falls.  In  fact,  if  the  entire  energy  of  the  discharge  is 
expended  in  producing  heat,  and  in  doing  no  other  kind 
of  work,  then  the  heat  developed  will  be  the  thermal 

*  This  instrument  differs  in  no  essential  respect  from  that  devised 
ninety  years  later  by  Riess,  to  whom  the  instrument  is  often  accredited. 
Riess,  however,  deduced  quantitative  laws,  while  Kinnersley  contented 
himself  with  qualitative  observations. 


CHAP,  iv  LUMINOUS  DISCHARGES  303 

Q,V 

equivalent  of  ^QV  ergs,  or  |jr  calories;  where  J  re- 
presents the  mechanical  equivalent  of  heat  (J  =  42 
million ;  since  42  x  106  ergs  =  1  calorie),  and  Q  and  V 
are  expressed  in  C.G.S.  units. 

When  a  powerful  discharge  takes  place  through  very 
thin  wires,  they  may  be  heated  to  redness,  and  even  fused 
by  the  heat  evolved.  Van  Marum  thus  once  heated  70 
feet  of  wire  by  a  powerful  discharge.  A  narrow  strip  of 
tinfoil  is  readily  fused  by  the  charge  of  a  large  Leydeii 
jar,  or  battery  of  jars.  A  piece  of  gold  leaf  is  in  like 
manner  volatilized  by  a  powerful  discharge.  Franklin 
utilized  this  property  for  a  rude  process  of  multiplying 
portraits  or  other  patterns,  which,  being  first  cut  out  in 
card,  wer6  reproduced  in  a  silhouette  of  metallic  particles 
on  a  second  card,  by  the  device  of  laying  above  them  a 
film  of  gold  or  silver  leaf  covered  again  with  a  piece  of 
card  or  paper ;  a  Leyden  battery  being  then  discharged 
through  the  leaf. 

318.  Luminous  Effects.  —  The  discharge  exhibits 
many  beautiful  and  varied  luminous  effects  under  dif- 
ferent conditions.  The  spark  of  the  disruptive  discharge 
is  usually  a  thin  brilliant  streak  of  light.  When  it  takes 
place  between  two  metallic  balls,  separated  only  by  a 
short  interval,  it  usually  appears  as  a  single  thin  and 
brilliant  line.  If,  however,  the  distance  be  as  much  as  a 
few  centimetres,  the  spark  takes  an  irregular  zig-zag  form. 
In  any  case  its  path  is  along  the  line  of  least  resistance, 
the  presence  of  minute  motes  of  dust  floating  in  the  air 
being  quite  sufficient  to  determine  the  zig-zag  character. 
Often  the  spark  exhibits  curious  ramifications  and  fork- 
ings,  of  which  an  illustration  is  given  in  Fig.  163,  which 
is  drawn  of  one-eighth  of  the  actual  size  of  the  spark 
obtained  from  an  electrical  machine.  Photographs  of 
lightning  flashes  almost  always  show  similar  branching. 
The  branches  always  point  toward  the  negative  electrode. 
The  discharge  from  a  Leyden  jar  affords  a  much  brighter, 


304  ELECTRICITY   AND   MAGNETISM      PART  n 

shorter,  noisier  spark  than  the  spark  drawn  direct  from 
the  collector  of  a  machine.  The  length  (see  Art.  313) 
depends  upon  the  potential,  and  upon  the  pressure  and 
temperature  of  the  air  in  which  the  discharge  takes  place. 
The  brilliance  depends  chiefly  upon  the  quantity  of  the 
discharge.  The  colour  of  the  spark  varies  with  the  na- 
ture of  the  metal  surfaces  between  which  the  discharge 


Fig.  163. 

takes  place ;  for  the  spark  tears  away  in  its  passage  small 
portions  of  the  metal  surfaces,  and  volatilizes  them. 
Between  copper  or  silver  terminals  the  spark  takes  a 
green  tint,  while  between  iron  knobs  it  is  of  a  reddish 
hue.  Examination  with  the  spectroscope  reveals  the 
presence  in  the  spark  of  the  rays  characteristic  of  the 
incandescent  vapours  of  the  several  metals. 

319.  Brush  Discharge  :  Glow  Discharge.  —  If  an  elec- 
tric machine  is  vigorously  worked,  but  no  sparks  be 
drawn  from  its  collector,  a  fine  diverging  brush  of  pale 
blue  light  can  be  seen  (in  a  dark  room)  streaming  from 
the  brass  ball  at  the  end  of  it  farthest  from  the  col- 
lecting comb ;  a  hissing  or  crackling  sound  always  accom- 
panies this  kind  of  discharge.  The  brush  discharge 
consists  of  innumerable  fine  twig-like  ramifications,  pre- 
senting a  form  of  which  Fig.  164  gives  a  fine  example. 
The  brightness  and  size  of  the  brush  is  increased  by 
holding  a  flat  plate  of  metal  a  little  way  from  it.  With 


CHAV.  iv  BRUSH    AND   GLOW  305 

a  smaller  ball,  or  with  a  bluntly-pointed  wire,  the  brush 
appears  smaller,  but  is  more  distinct  and  continuous. 
When  discharge  is  going  on  between  two  balls  the 
brushes  are  never  alike.  At  the  positive  ball  or  anode 
the  brush  discharge  is  larger  and  more  ramified  than  at 
the  negative  ball.  But  the  negative  brush  is  more  easily 
formed  than  the  positive.  Wheatstone  found  by  using  his 
rotating  mirror  that  the  brush  discharge  is  really  a  series 


Fig.  164. 

of  successive  partial  sparks  at  rapid  intervals.  Metallic 
dust  is  in  every  case  torn  away  from  the  electrode  by  the 
brush  discharge. 

If  the  blunt  or  rounded  conductor  be  replaced  by  a 
pointed  one,  the  brush  disappears  and  gives  place  to  a 
quiet  and  continuous  glow  where  the  electrified  particles 
of  air  are  streaming  away  at  the  point.  If  these  con- 
vexion  streams  are  impeded  the  glow  may  once  more 
give  place  to  the  brush.  Where  a  negative  charge  is 
being  discharged  at  a  point,  the  glow  often  appears  to 
be  separated  from  the  surface  of  the  conductor  by  a  dark 
space,  where  the  air,  without  becoming  luminous,  still 


300  ELECTRICITY   AND   MAGNETISM      PART  n 

conveys  the  electricity.  This  phenomenon,  to  which 
Faraday  gave  the  name  of  the  "  dark  "  discharge,  is  very 
well  seen  when  electricity  is  discharged  through  rarefied 
air  and  other  gases  in  vacuum  tubes. 

A  spark  discharge  may  degenerate  into  a  brush  if  the 
surface  of  the  electrode  becomes  pitted  or  roughened  by 
frequent  discharges.  Hence  in  all  spark  experiments  it  is 
important  to  keep  the  discharging  balls  highly  polished. 

320.  Discharges  in  Partial  Vacua.  —  If  the  discharge 
takes  place  in  glass  tubes  or  vessels  from  which  the  air 
has  been  partially  exhausted,  many  remarkable  and  beau- 
tiful luminous  phenomena  are  produced.  A  common 
form  of  vessel  is  the  "electric  egg"  (Fig.  137),  a  sort  of 
oval  bottle  that  can  be  screwed  to  an  air  pump,  and 


Fig.  165. 

furnished  with  brass  knobs  to  lead  in  the  sparks.  More 
often  "vacuum  tubes,"  such  as  those  manufactured  by 
the  celebrated  Geissler,  are  employed.  These  are  merely 
tubes  of  thin  glass  blown  into  bulbous  or  spiral  forms, 
provided  with  two  electrodes  of  platinum  wire  fused  into 
the  glass,  and  sealed  off  after  being  partially  exhausted 
of  air  by  a  mercurial  air  pump.  Of  these  Geissler  tubes 
the  most  useful  consist  of  two  bulbs  joined  by  a  narrow 
tube  (Fig.  165),  the  luminous  effects  being  usually  more 
intense  in  the  contracted  portion.  Such  tubes  are  readily 
illuminated  by  discharges  from  an  electrophorus  or  an 


CHAP,  iv  VACUUM    TUBES  307 

influence  machine ;  but  it  is  more  common  to  work  them 
with  the  spark  of  an  induction  coil  (Fig.  135).  A  coil 
capable  of  throwing  a  i-inch  spark  in  air  will  illuminate 
a  vacuum  tube  6  or  8  inches  long.  Wheie  an  alternate- 
current  supply  is  available  small  transformers  (Art.  228) 
wound  to  deliver  fa  ampere  at  5000  volts  serve  admirably 
for  lighting  vacuum  tubes. 

Through  such  tubes,  before  exhaustion,  the  spark 
passes  without  any  unusual  phenomena  being  produced. 
As  the  air  is  exhausted  the  sparks  become  less  sharply 
defined,  and  widen  out  to  occupy  the  whole  tube,  becom- 
ing pale  in  tint  and  nebulous  in  form.  The  kathode 
exhibits  a  beautiful  bluish  or  violet  glow,  separated  from 
the  conductor  by  a  narrow  dark  space,  while  at  the  anode 
a  single  small  bright  star  of  light  is  all  that  remains. 
At  a  certain  degree  of  exhaustion  the  light  in  the  tube 
breaks  up  into  a  set  of  strice,  or  patches  of  light  of  a  cup- 
like  form,  which  vibrate  to  and  fro  between  darker  spaces. 
In  nitrogen  gas  the  violet  aureole  glowing  around  the 
kathode  is  very  bright,  the  rest  of  the  light  being  rosy 
in  tint.  In  oxygen  the  difference  is  not  so  marked.  In 
hydrogen  gas  the  tint  of  the  discharge  is  bluish,  except 
where  the  tube  is  narrow,  where  a  beautiful  crimson  may 
be  seen.  With  carbonic  acid  gas  the  light  is  remarkably 
white.  Particles  of  metal  are  torn  off  from  the  kathode, 
and  projected  from  its  surface.  The  kathode  is  also  usu- 
ally the  hotter  when  made  of  similar  dimensions  to  the 
anode.  If  the  anode  is  heated  and  the  kathode  kept 
cool  no  discharge  will  pass.  The  luminosity  disappears 
from  the  rarefied  air  in  the  neighbourhood  of  a  red-hot 
platinum  spiral  inside  the  tube.  If  the  kathode  gets 
white-hot  the  glow  disappears,  and  the  gas  conducts 
freely  without  shining.  It  is  also  observed  that  the  light 
of  these  discharges  in  vacuo  is  rich  in  those  rays  which 
produce  phosphorescence  and  fluorescence.  Many  beau- 
tiful effects  are  therefore  produced  by  blowing  tubes  in 
uranium  glass,  which  fluoresces  with  a  fine  green  light, 


308  ELECTRICITY   AND   MAGNETISM       PART  n 

and  by  placing  solutions  of  quinine  or  other  fluorescent 
liquids  in  outer  tubes  of  glass. 

321.  Phenomena  in  High  Vacua.  —  Crookes  has  found 
that  when  exhaustion  is  carried  to  a  very  high  degree  the 
dark  space  separating  the  negative  glow  from  the  negative 
pole  increases  in  width;  and  that  across  this  space  elec- 
trified molecules  are  projected  in  parallel  paths  normally 
from  the  surface  of  the  kathode.  If  exhaustion  be  carried 
to  such  a  high  degree  that  the  dark  space  fills  the  entire 
tube  or  bulb,  the  glass  walls  become  beautifully  phos- 
phorescent. Diamonds,  rubies,  and  even  white  powdered 

alumina  placed  in  the 
tubes  become  brill- 
iantly phosphorescent 
if  the  kathode  dis- 
charge is  directed  upon 
them.  And  if  bodies 
(whether  opaque  or 
transparent)  be  inter- 
posed in  front  of  the 
electrode,  sharply-de- 
fined  shadows  of  these 
bodies  are  projected 

upon  the  opposite  wall  of  the  vessel,  as  if  they  stopped 
the  way  for  some  of  the  flying  molecules,  and  prevented 
them  from  striking  the  opposite  wall.  In  Fig.  166  the 
kathode  K  is  a  slightly  convex  disk  of  aluminium.  In 
the  path  of  the  discharge  is  set  a  cross  cut  out  of  mica. 
Its  shadow  S  appears  on  the  end  of  the  bulb,  which  phos- 
phoresces all  around  the  shadowed  part.  The  anode  may 
be  either  at  A  or  a.  Lightly-poised  vanes  are  also  driven 
round  if  placed  in  the  path  of  the  discharge.  Crookes 
regarded  this  kathode  discharge  as  exhibiting  matter  in 
an  ultra-gaseous  or  radiant  state.  A  disk  placed  in  the 
line  of  the  kathode  discharge  becomes  thereby  posi- 
tively electrified.  The  kathode  discharge  is  independent 
of  the  metal  used  as  kathode,  and  is  also  independent  of 


CHAP,  iv          EFFECTS   IN   HIGH   VACUA  309 

the  position  of  the  anode.  Any  restriction  of  space 
around  the  kathode  tends  to  stop  the  discharge.  Similar 
phenomena  have  been  observed  in  vacuous  tubes  without 
any  internal  electrodes.  Hertz  discovered  that  these 
kathodic  "  rays  "  which  will  not  pass  through  glass,  mica, 
or  any  transparent  substance,  will  pass  through  metal 
foil.  Lenard,  using  a  vacuum  tube  with  a  "  window  "  of 
aluminium  foil  at  one  end,  has  succeeded  in  passing  the 
kathodic  rays  out  into  the  air  (in  which  they  cannot 
be  produced  at  all),  and  finds  them  to  retain  their  re- 
markable property  of  exciting  phosphorescence. 

In  extremely  high  vacua  there  is  an  enormous  re- 
sistance, apparently  due  to  some  difficulty  in  the  electric 
discharge  leaving  the  electrode.  The  molecular  con- 
ductivity of  the  rarefied  gas  is  itself  very  high.  For 
an  equal  number  of  molecules  it  is  higher  than  that  of 
the  metals. 

Holtz  has  more  recently  produced  "  electric  shadows," 
by  means  of  discharges  in  air  at  ordinary  pressure,  be- 
tween the  poles  of  the  influence  machine  (Fig.  41),  the 
discharge  taking  place  between  a  point  and  a  disk  covered 
with  silk,  on  which  the  shadows  are  thrown. 

322.  Striae.  —  The  striae  or  stratifications  have  been 
examined  very  carefully  by  Gassiot,  by  Spottiswoode,  and 
by  De  la  Rue.  The  principal  facts  hitherto  gleaned  are 
as  follow  :  —  The  striae  originate  at  the  anode  at  a  certain 
pressure,  and  become  more  numerous,  as  the  exhaustion 
proceeds,  up  to  a  certain  point,  when  they  become  thicker 
and  diminish  in  number,  until  exhaustion  is  carried  to 
such  a  point  that  no  discharge  will  pass.  J.  J.  Thomson 
found  the  column  of  striae  to  exhibit  a  nearly  constant 
electric  resistance  all  along ;  though  beyond  it  in  the 
neighbourhood  of  the  kathode  the  resistance  was  much 
greater.  In  a  vacuum  tube  over  50  feet  long  the  dis- 
charge was  striated  through  whole  length  except  near  the 
kathode.  If  the  kathode  is  moved  forward  the  striae 
move  with  it.  The  striae  flicker  even  when  the  con- 


310  ELECTRICITY   AND   MAGNETISM      PART  n 


tinuous  current  from  a  battery  of  some  thousands  of  cells 
(Art.  18G)  is  used.  There  is  a  maximum  of  steadiness 
with  a  particular  density  of  current.  The  striae  are  hotter 
than  the  spaces  between  them.  The  number  and  position 
of  the  striae  vary,  not  only  with  the  exhaustion,  but  with 
the  difference  of  potentials  of  the  electrodes.  Each  portion 
of  the  column  of  striae  acts  as  an  independent  discharge. 
When  striae  are  produced  by  the  intermittent  discharges 
of  the  induction  coil,  examination  of  them  in  a  rotating 
mirror  reveals  that  they  move  forward  from  the  anode 
towards  the  kathode. 

Schuster  has  shown  that  the  discharge  through  gases 
is  a  process  resembling  that  of  electrolysis  (Art.  237), 
being  accompanied  by  breaking  up  of  the  gaseous  mole- 
cules and  incessant  interchanges  of  atoms  between  them. 
The  production  of  ozone  (Art.  316)  and  the  phenomena 
noticed  at  the  kathode  (Art.  321)  give  support  to  this 
view.  Amongst  other  evidence  is  the  striking  discovery 
of  Hittorf  that  quite  a  few  cells  can  send  a  current 
through  gas  at  ordinary  pressures  provided  a  spark-dis- 
charge is  going  on  in  the  neighbourhood.  J.  J.  Thomson 
finds  that  those  gases  which  when  heated  are  decomposed 
or  molecularly  dissociated,  so  that  free  atoms  are  present, 
are  also  good  conductors.  He  regards  chemical  decom- 
position as  an  essential  feature  of  gaseous  discharge. 

The  discharges  in  vacuum  tubes  are  affected  by  the 
magnet  at  all  degrees  of  exhaustion,  behaving  like  flexible 
conductors.  Under  certain  conditions  also,  the  discharge 
is  sensitive  to  the  presence  of  a  conductor  on  the  exterior 
of  the  tube,  retreating  from  the  side  where  it  is  touched. 
This  sensitive  state  appears  to  be  due  to  a  periodic  inter- 
mittence  in  the  discharge;  an  intermittence  or  partial 
intermittence  in  the  flow  would  also  probably  account  for 
the  production  of  striae. 

323.  Velocity  of  Propagation  of  Discharge. —The 
earliest  use  of  the  rotating  mirror  to  analyze  pheno- 
mena of  short  duration  was  made  by  Wheatstone,  who 


CHAP,  iv       VELOCITY   OF  PROPAGATION  311 

attempted  by  this  means  to  measure  "  the  velocity  of 
electricity"  in  conducting  wires.  What  he  succeeded  in 
measuring  was  not,  however,  the  velocity  of  electricity,  but 
the  time  taken  by  a  certain  quantity  of  electricity  to 
flow  through  a  conductor  of  considerable  resistance  and 
capacity.  Viewed  in  a  rotating  mirror,  a  spark  of  definite 
duration  would  appear  to  be  drawn  out  into  an  elongated 
streak.  Such  an  elongation  was  found  to  be  visible  when 
a  Ley  den  jar  was  discharged  through  a  copper  wire  half 
a  mile  long;  and  when  the  circuit  was  interrupted  at 
three  points,  one  in  the  middle  and  one  at  each  end  of  this 
wire,  three  sparks  were  obtained,  which,  viewed  in  the 
mirror,  showed  a  lateral  displacement,  indicating  (with 
the  particular  rate  of  rotation  employed)  that  the  middle 
spark  took  place  TIT!O¥O  °f  a  second  later  than  those  at  the 
ends.  Wheatstone  argued  from  this  a  velocity  of  288,000 
miles  per  second.  But  Faraday  showed  that  the  apparent 
rate  of  propagation  of  a  quantity  of  electricity  must  be 
affected  by  the  capacity  of  the  conductor ;  and  he  even 
predicted  that  since  a  submerged  insulated  cable  acts  like 
a  Leyden  jar  (see  Art.  301),  and  has  to  be  charged  before 
the  potential  at  the  distant  end  can  rise,  it  will  retard 
the  apparent  flow  of  electricity  through  it.  Professor 
Fleeming  Jenkin  says  of  one  of  the  Atlantic  cables  that, 
after  contact  with  the  battery  is  made  at  one  end,  no 
effect  can  be  detected  at  the  other  for  two-tenths  of  a 
second,  and  that  then  the  received  current  gradually 
increases,  until  about  three  seconds  afterwards  it  reaches 
its  maximum,  and  then  dies  away.  This  retardation  is 
proportional  to  the  square  of  the  length  of  the  cable,  being- 
proportional  both  to  its  capacity  and  to  its  resistance; 
hence  it  becomes  very  serious  on  long  cables,  reducing  the 
speed  of  signalling.  There  is  in  fact  no  definite  assign- 
able "  velocity  of  electricity."  In  the  case  of  wires 
suspended  in  air  the  velocity  of  propagation  of  any  rapid 
electrical  vibration  is  equal  to  the  velocity  of  light.  But 
in  the  case  of  slow  vibrations,  like  those  of  telephonic 


312  ELECTRICITY  AND   MAGNETISM      PART  n 

sounds  being  sent  through  land  lines  or  cables,  the  velo- 
city may  be  much  less. 

A  very  simple  experiment  will  enable  the  student  to 
realize  the  excessively  short  duration  of  the  spark  of  a 
Leyden  jar.  Let  a  round  disk  of  cardboard  painted 
with  black  and  white  sectors  be  rotated  very  rapidly  so 
as  to  look  by  ordinary  light  like  a  mere  gray  surface. 
When  this  is  illuminated  by  the  spark  of  a  Leyden  jar  it 
appears  to  be  standing  absolutely  still,  however  rapidly 
it  may  be  turning.  A  flash  of  lightning  is  equally  in- 
stantaneous; it  is  utterly  impossible  to  determine  at 
which  end  the  flash  begins.* 

324.  Electric  Dust-Figures.  —  Electricity  may  creep 
slowly  over  the  surface  of  bad  conductors.  Lichtenberg 


Fig.  167. 

devised  an  ingenious  and  easy  way  of  investigating  the 

*  Sometimes  the  flash  seems  to  strike  downwards  from  the  clouds,  some- 
times upwards  from  the  earth.  This  is  an  optical  illusion,  resulting 
from  the  unequal  sensitiveness  to  light  of  different  portions  of  the  retina  of 
the  eve. 


CHAP.    IV 


ELECTRIC   DUST-FIGURES 


313 


distribution  of  electricity  by  means  of  certain  electro- 
scopic  powders.  Take  a  charged  Leyden  jar  an.d  write 
with  the  knob  of  it  upon  a  cake  of  pitch  or  a  dry  sheet  of 
glass.  Then  sift,  through  a  bit  of  muslin,  over  the  cake 
a  mixture  of  powdered  red  lead  and  sulphur  (vermilion 
and  lycopodium  powder  answer  equally  well).  The 
powders  in  this  process  rub  against  one  another,  the  red 
lead  becoming  -f,  the  sulphur  — .  Hence  the  sulphur  will 


be  attracted  to  those  parts  where  there  is  +  electrification 
on  the  disk,  and  settles  down  in  curious  branching  yellow 
streaks  like  those  shown  in  Fig.  167.  The  red  lead  settles 
down  in  little  red  heaps  and  patches  where  the  electrifica- 
tion is  negative.  These  rounded  red  patches  indicate  that 
the  —  discharge  has  been  of  the  nature  of  a  wind  or  silent 
discharge.  The  branching  yellow  streaks  indicate  that 
the  positive  discharge  (as  indeed  may  be  heard)  is  of  the 
nature  of  a  brush.  Fig.  108  shows  the  general  appearance 
of  the  Lichtenberg's  figure  produced  by  holding  the  knob 


314  ELECTKIC1TY    AND    MAGNETISM      PART  n 

of  the  Ley  den  jar  at  the  centre  of  a  shellac  plate  that  has 
previously  been  rubbed  with  flannel,  the  negative  elec- 
trification being  attracted  upon  all  sides  toward  the 
central  positive  charge.  These  same  powders  may  be  used 
to  investigate  how  surfaces  have  become  electrified  by 
rubbing,  and  how  pyroelectric  crystals  (Art.  74)  are  elec- 
trified during  cooling. 

Powdered  tourmaline,  warmed  and  then  sifted  over  a 
sheet  of  glass  previously  electrified  irregularly,  will  show 
similar  figures,  though  not  so  well  defined. 

Breath-figures  can  be  made  by  electrifying  a  coin  or 
other  piece  of  metal  laid  upon  a  sheet  of  dry  glass,  and 
then  breathing  upon  the  glass  where  the  coin  lay,  reveal- 
ing a  faint  image  of  it  on  the  surface  of  the  glass. 

F.  J.  Smith  finds  that  if  a  coin  or  engraving  laid  face- 
down upon  a  photographic  dry-plate  is  sparked  with  an 
induction  coil,  the  plate  receives  an  invisible  image  which 
can  be  photographically  developed. 

325.  Physiological  Effects.—  The  physiological  effects 
of  the  current  have  been  described  in  Lesson  XX.    Those 
produced  by   the   spark-discharge   are    more  sudden    in 
character,   but   of   the   same  general  nature.      Death    is 
seldom  the  direct  result.      The   shock  causes  a  sudden 
cessation  of  respiration,  resulting  in  suffocation  as  from 
drowning.    The  bodies  of  persons  struck  by  the  lightning 
spark  frequently  exhibit  markings  of  a  reddish  tint  where 
the  discharge  in  passing  through  the  tissues  has  lacerated 
or  destroyed  them.     Sometimes  these  markings  present 
a  singular  ramified  appearance,  as  though  the  discharge 
had  spread  in  streams  over  the  surface  at  its  entry. 

326.  Dissipation  of  Charge.  —  However  well  insu- 
lated a  charged  conductor  may  be,  and  however  dry  the 
surrounding  air,  it  nevertheless  slowly  loses  its  charge, 
and  in  a  few  days  will  be  found  to  be  completely  discharged. 
The  rate  of  loss  of  charge  is,  however,  not  uniform.     It 
is  approximately  proportional  to  the  difference  of  potential 
between  the  body  and  the  earth.     Hence  the  rate  of  loss 


CHAP,   iv  LAW   OF   LEAKAGE  315 

is  greater  at  first  than  afterwards,  and  is  greater  for 
highly-charged  bodies  than  for  those  feebly  charged.  The 
law  of  dissipation  of  charge  therefore  resembles  Newton's 
law  of  cooling,  according  to  which  the  rate  of  cooling  of  a 
hot  body  is  proportional  to  the  difference  of  temperature 
between  it  and  the  surrounding  objects.  If  the  potential 
of  the  body  be  measured  at  equal  intervals  of  time  it  will 
be  found  to  have  diminished  in  a  decreasing  geometric 
series;  or  the  logarithms  of  the  potentials  at  equal  in- 
tervals of  time  will  differ  by  equal  amounts.  The  rate 
of  loss  is,  however,  greater  at  negatively-electrified  sur- 
faces than  at  positive. 

This  may  be  represented  by  the  following  equation :  — 
V,  =  \V  P', 

where  V0  represents  the  original  potential  and  V«  the  potential 
after  an  intervall.  Here  c  stands  for  the  number  2-71828  .  .  . 
(the  base  of  the  natural  logarithms),  and  p  stands  for  the 
"  coefficient  of  leakage,"  which  depends  upon  the  temperature, 
pressure,  and  humidity  of  the  air.  The  same  formula  serves  for 
the  discharge  of  a  condenser  of  capacity  K  through  a  resistance 
R;  if  p  is  written  for  1/KR. 

327.  Positive  and  Negative  Electrification.  —  The 
student  will  not  have  failed  to  notice  throughout  this 
lesson  frequent  differences  between  the  behaviour  of 
positive  and  negative  electrification.  The  striking  dis- 
similarity in  the  Lichtenberg's  figures,  the  displacement 
of  the  perforation-point  in  Lullin's  experiment,  the  un- 
equal tendency  to  dissipation  at  surfaces,  the  unequal 
action  of  heat  on  positive  and  negative  charges,  the  re- 
markable differences  in  the  various  forms  of  brush  and 
glow  discharge,  are  all  points  that  claim  attention.  Gas- 
siot  described  the  appearance  in  vacuum  tubes  as  of  a 
force  emanating  from  the  negative  pole.  Crookes's  experi- 
ments in  high  vacua  show  molecules  to  be  violently 
discharged  from  the  negative  electrode,  the  vanes  of  a 
little  fly  enclosed  in  such  tubes  being  moved  from  the 
side  struck  by  the  negative  discharge.  Holtz  found  that 


316  ELECTRICITY   AND    MAGNETISM      PART  n 

when  funnel-like  partitions  were  fixed  in  a  vacuum  tube 
the  resistance  is  much  less  when  the  open  mouths  of  the 
funnels  face  the  negative  electrode.  These  matters  are 
yet  quite  unaccounted  for  by  any  existing  theory  of 
electricity. 

The  author  of  these  lessons  is  disposed  to  take  the  following 
view  on  this  point:  —  If  electricity  be  really  one  and  not  two, 
either  the  so-called  positive  or  the  negative  electrification  must 
be  a  state  in  which  there  is  more  electricity  than  in  the  sur- 
rounding space,  and  the  other  must  be  a  state  in  which  there  is 
less.  The  student  was  told,  in  Art.  7,  that  in  the  present  state 
of  the  science  we  do  not  know  for  certain  whether  "  positive" 
electrification  is  really  an  excess  of  electricity  or  a  defect.  Now 
some  of  the  phenomena  alluded  to  in  this  Article  seem  to  in- 
dicate that  the  so-called  " negative"  electrification  really  is  the 
state  of  excess.  In  particular,  the  fact  that  the  rate  of  dissipation 
of  charge  is  greater  for  negative  electrification  than  for  positive, 
points  this  way ;  because  the  law  of  loss  of  charge  is  the  exact 
counterpart  of  the  law  of  the  loss  of  heat,  in  which  it  is  quite  cer- 
tain that,  for  equal  differences  of  temperature  between  a  body 
and  its  surroundings,  the  rate  of  loss  of  heat  is  greater  at  higher 
temperatures  than  at  lower ;  or  the  body  that  is  really  hotter 
loses  its  heat  fastest. 


LESSON  XXV.  —  Atmospheric  Electricity 

328.  The  phenomena  of  atmospheric  electricity  are 
of  two  kinds.    There  are  the  well-known  electrical  pheno- 
mena of  thunderstorms ;    and  there  are  the  phenomena 
of  continual  slight  electrification  in  the  air,  best  observed 
when  the  weather  is  fine.    The  phenomena  of  the  Aurora 
constitute  a  third  branch  of  the  subject. 

329.  The  Thunderstorm  an  Electrical   Phenomenon. 
—  The  detonating  sparks  drawn  from  electrical  machines 
and  from  Leyden  jars   did   not  fail  to  suggest  to  the 
early  experimenters,  Hauksbee,  Newton,  Wall,  Nollet, 
and    Gray,   that   the   lightning   flash   and  the   thunder- 
clap were  due  to  electric  discharges.     In  1749,  Benja- 
min Franklin,  observing  lightning  to  possess  almost  all 


CHAP,  iv  THUNDERSTORMS  317 

the  properties  observable  in  electric  sparks,*  suggested 
that  the  electric  action  of  points  (Art.  46),  which  was 
discovered  by  him,  might  be  tried  on  thunderclouds,  and 
so  draw  from  them  a  charge  of  electricity.  He  proposed, 
therefore,  to  fix  a  pointed  iron  rod  to  a  high  tower. 
Before  Franklin  could  carry  his  proposal  into  effect, 
Dalibard,  at  Marly-la-ville,  near  Paris,  taking  up  the 
hint,  erected  an  iron  rod  40  feet  high,  by  which,  in  1752, 
he  drew  sparks  from  a  passing  cloud.  Franklin  shortly 
after  succeeded  in  another  way.  He  sent  up  a  kite  during 
the  passing  of  a  storm,  and  found  the  wetted  string  to 
conduct  electricity  to  the  earth,  and  to  yield  abundance 
of  sparks.  These  he  drew  from  a  key  tied  to  the  string, 
a  silk  ribbon  being  interposed  between  his  hand  and  the 
key  for  safety.  Leyden  jars  could  be  charged,  and  all 
other  electrical  effects  produced,  by  the  sparks  furnished 
from  the  clouds.  The  proof  of  the  identity  was  complete. 
The  kite  experiment  was  repeated  by  Romas,  who  drew 
from  a  metallic  string  sparks  9  feet  long,  and  by  Cavallo, 
who  made  many  important  observations  on  atmospheric 
electricity.  In  1753  Richmann,  of  St.  Petersburg,  who 
was  experimenting  with  an  apparatus  resembling  that 
of  Dalibard,  was  struck  by  a  sudden  discharge  and 
killed. 

330.  Theory  of  Thunderstorms.  —  Solids  and  liquids 
cannot  be  charged  throughout  their  substance  ;  if  charged 
at  all  the  electrification  is  upon  their  surface  (see  Art. 
41).  But  gases  and  vapours,  being  composed  of  myriads 

*  Franklin  enumerates  specifically  an  agreement  between  electricity  and 
lightning  in  the  following  respects  :  —  Giving  light ;  colour  of  the  light ; 
crooked  direction ;  swift  motion  ;  being  conducted  by  metals ;  noise  in 
exploding  ;  conductivity  in  water  and  ice ;  rending  imperfect  conductors ; 
destroying  animals ;  melting  metals ;  firing  inflammable  substances ;  sul- 
phureous smell  (due  to  ozone,  as  we  now  know) ;  and  he  had  previously 
found  that  needles  could  be  magnetized  both  by  lightning  and  by  the 
electric  spark.  He  also  drew  attention  to  the  similarity  between  the  pale- 
blue  flame  seen  during  thundery  weather  playing  at  the  tips  of  the  masts 
of  ships  (called  by  sailors  St.  Elmo's  Fire),  and  the  "glow  "  discharge  at 
points. 


318  ELECTRICITY   AND   MAGNETISM      PART  n 

of  separate  particles,  can  receive  a  bodily  charge.  The 
air  in  a  room  in  which  an  electric  machine  is  worked 
is  found  afterwards  to  be  charged.  The  clouds  are 
usually  charged  more  or  less  with  electricity,  derived, 
probably,  from  evaporation  going  on  at  the  earth's  surface. 
The  minute  particles  of  water  floating  in  the  air  become 
more  highly  charged.  As  they  fall  by  gravitation  and 
unite  together,  the  strength  of  their  charges  increases. 
Suppose  eight  small  drops  to  join  into  one.  That  one 
will  have  eight  times  the  quantity  of  electricity  dis- 
tributed over  the  surface  of  a  single  sphere  of  twice  the 
radius  (and,  therefore,  of  twice  the  capacity,  by  Art.  27l2) 
of  the  original  drops;  and  its  electrical  potential  will 
therefore  be  four  times  as  great.  Now  a  mass  of  cloud 
may  consist  of  such  charged  spheroids,  and  its  potential 
may  gradually  rise,  therefore,  by  the  coalescence  of  the 
drops,  and  the  electrification  at  the  lower  surface  of  the 
cloud  will  become  greater  and  greater,  the  surface  of 
the  earth  beneath  acting  as  a  condensing  plate  and  becom- 
ing charged,  by  influence,  with  the  opposite  kind  of  elec- 
trification. Presently  the  difference  of  potential  becomes 
so  great  that  the  intervening  strata  of  air  give  way  under 
the  strain,  and  a  disruptive  discharge  takes  place  at  the 
point  where  the  air  offers  least  resistance.  This  lightning- 
spark,  which  may  be  more  than  a  mile  in  length,  dis- 
charges only  the  electricity  that  has  been  accumulating 
at  the  surface  of  the  cloud,  and  the  other  parts  of  the 
cloud  will  now  react  upon  the  discharged  portion,  pro- 
ducing internal  attractions  and  internal  discharges.  The 
internal  actions  thus  set  up  will  account  for  the  usual 
appearance  of  a  thundercloud,  that  it  is  a  well-defined 
flat-bottomed  mass  of  cloud  which  appears  at  the  top  to 
be  boiling  or  heaving  up  with  continual  movements. 

331.  Lightning  and  Thunder.  —  Three  kinds  of 
lightning  have  been  distinguished  by  Arago :  (i.)  The 
Zig-zag  flash  or  "Forked  lightning,"  of  ordinary  occur- 
rence. The  zig-zag  form  is  probably  due  either  to  the 


CHAP,  iv  LIGHTNING   FLASHES  .319 

presence  of  solid  particles  in  the  air  or  to  local  electrifi- 
cation at  certain  points,  making  the  crooked  path  the  one 
of  least  resistance,  (ii.)  Sheet  lightning,  in  which  whole 
surfaces  are  lit  up  at  once,  is  probably  only  the  reflexion 
on  the  clouds  of  a  flash  taking  place  at  some  other  part 
of  the  sky.  It  is  often  seen  on  the  horizon  at  night, 
reflected  from  a  storm  too  far  away  to  produce  audible 
thunder,  and  is  then  known  as  "summer  lightning." 
(iii.)  Globular  lightning,  in  the  form  of  balls  of  jire,  which 
move  slowly  along  and  then  burst  with  a  sudden  ex- 
plosion. This  form  is  very  rare,  but  must  be  admitted 
as  a  real  phenomenon,  though  some  of  the  accounts  of  it 
are  greatly  exaggerated.  Similar  phenomena  on  a  small 
scale  have  been  produced  (though  usually  accidentally) 
with  electrical  apparatus. 

The  sound  of  the  thunder  may  vary  with  the  con- 
ditions of  the  lightning  spark.  The  spark  heats  the  air 
in  its  path,  causing  sudden  expansion  and  compression 
all  round,  followed  by  as  sudden  a  rush  of  air  into  the 
partial  vacuum  thus  produced.  If  the  spark  be  straight 
and  short,  the  observer  will  hear  but  one  short  sharp  cla/>. 
If  its  path  be  a  long  one  and  not  straight,  he  will  hear 
the  successive  sounds  one  after  the  other,  with  a  charac- 
teristic rattle,  and  the  echoes  from  other  clouds  will  come 
rolling  in  long  afterwards.  The  lightning-flash  itself 
never  lasts  more  than  TQ  oWo  °f  a  second,  but  sometimes 
is  oscillatory  in  character  (see  Art.  515). 

The  damage  done  by  a  lightning-flash  when  it  strikes 
an  imperfect  conductor  appears  sometimes  as  a  disrup- 
tive mechanical  disintegration,  as  when  the  masonry  of  a 
chimney-stack  or  church-spire  is  overthrown,  and  some- 
times as  an  effect  of  heat,  as  when  bell-wires  and  pbjects 
of  metal  in  the  path  of  the  lightning-current  are  fused. 
The  physiological  effects  of  sudden  discharges  are  dis- 
cussed in  Arts.  255  and  325. 

The  "  return-stroke  "  experienced  by  persons  in  the 
neighbourhood  of  a  flash  is  explained  in  Art.  29. 


320  ELECTRICITY    AND   MAGNETISM      PART  11 

332.  Lightning  Conductors.  —  The  first  suggestion 
to  protect  property  from  destruction  by  lightning  was 
made  by  Franklin  in  1749,  in  the  following  words  :  — 

"  May  not  the  knowledge  of  this  power  of  points  be  of  use  to 
mankind,  in  preserving  houses,  churches,  ships,  etc.,  from  the 
stroke  of  lightning,  by  directing  us  to  fix  on  the  highest  parts  of 
those  edifices  upright  rods  of  iron  made  sharp  as  a  needle,  and 
gilt  to  prevent  rusting,  and  from  the  foot  of  those  rods  a  wire 
down  the  outside  of  the  building  into  the  ground,  or  round  one  of 
the  shrouds  of  a  ship,  and  down  her  side  till  it  reaches  the  water? 
Would  not  these  pointed  rods  probably  draw  the  electrical  fire 
silently  out  of  a  cloud  before  it  came  nigh  enough  to  strike,  and 
thereby  secure  us  from  that  most  sudden  and  terrible  mischief  ?  " 

Maxwell  proposed  to  cover  houses  with  a  network  of 
conducting  wires,  without  any  main  conductor,  the  idea 
being  that  then  the  interior  of  the  building  will,  like 
Faraday's  hollow  cube  (Art.  34),  be  completely  protected 
from  electric  force.  Much  controversy  has  arisen  of  late 
respecting  lightning-rods.  Professor  Oliver  Lodge  main- 
tains the  lightning  flash  to  be  of  the  nature  of  an  electric 
oscillation  (Art.  515)  rather  than  a  current.  If  so,  the 
conductor  of  least  resistance  is  not  necessarily  the  best 
lightning-rod.  Professor  Lodge  and  the  author  inde- 
pendently, and  for  different  reasons,  recommend  iron  in 
preference  to  copper  for  lightning-rods. 

The  following  points  summarize  the  modern  views  on 
the  subject :  — 

1.  All  parts  of  a  lightning  conductor  should  be  of  one  and 
the  same  metal,  avoiding  joints  as  far  as  possible,  and  with  as 
few  sharp  bends  or  corners  as  may  be. 

2.  The  use  of  copper  for  lightning-rods  is  a  needless  extrava- 
gance.   Iron  is  far  better.    Ribbon  is  slightly  better  than  round 
rod;  but  ordinary  galvanized  iron  telegraph-wire  is  good  enough. 

3.  The  conductor  should  terminate  not  merely  at  the  highest 
point  of  a  building,  but  be  carried  to  all  high  points.    It  is 
unwise  to  erect  very  tall  pointed  rods  projecting  several  feet 
above  the  roof. 

4.  A  good  deep  wet  "  earth  "  should  be  provided,  independent 
of  gas  or  water  pipes,  to  which  the  conductor  should  be  led  down. 


CHAP,  iv       ATMOSPHERIC   ELECTRICITY  321 

5.  If  in  any  part  the  conductor  goes  near  a  gas  or  water  pipe 
it  is  better  to  connect  them  metallically  than  to  leave  them  apart. 

6.  In  ordinary  buildings  the  conductor  should  be  insulated 
away  from  the  walls,  so  as  to  lessen  liability  of  lateral  discharge 
to  metal  stoves  and  things  inside  the  house. 

7.  Connect  all  external  metal-work,  zinc  spouts,  iron  crest 
ornaments,  and  the  like,  to  each  other,  and  to  the  earth,  but 
not  to  the  lightning  conductor. 

8.  The  cheapest  way  of  protecting  an  ordinary  house  is  to 
run  common  galvanized  iron  telegraph-wire  up  all  the  corners, 
along  all  the  ridges  and  eaves,  and  over  all  the  chimneys ;  tak- 
ing them  down  to  the  earth  in  several  places,  to  a  moist  stratum, 
and  at  each  place  burying  a  load  of  coke. 

9.  Over  the  tops  of  tall  chimneys  it  is  well  to  place  a  loop  or 
arch  of  the  lightning  conductor,  made  of  any  stout  and  durable 
metal. 

333.  Atmospheric  Electricity.  —  In  1752  Lemonnier 
observed  that  the  atmosphere  usually  was  in  an  electrical 
condition.  Cavallo,  Beccaria,  Ceca,  and  others,  added 
to  our  knowledge  of  the  subject,  and  more  recently 
Quetelet  and  Lord  Kelvin  have  generalized  from  more 
careful  observations.  The  main  result  is  that  the  air 
above  the  surface  of  the  earth  is  usually,  during  fine 
weather,  positively  electrified,  or  at  least  that  it  is 
positive  with  respect  to  the  earth's  surface,  the  earth's 
surface  being  relatively  negative.  The  so-called  measure- 
ments of  "atmospheric  electricity"  are  really  measure- 
ments of  difference  of  potential  between  a  point  of  the 
earth's  surface,  and  a  point  somewhere  in  the  air  above  it. 
In  the  upper  regions  of  the  atmosphere  the  air  is  highly 
rarefied,  and  conducts  like  the  rarefied  gases  in  Geissler's 
tubes  (Art.  320).  The  lower  air  is,  when  dry,  a  non- 
conductor. The  upper  stratum  is  believed  to  be  charged 
with  +  electricity,  while  the  earth's  surface  is  itself 
negatively  charged  ;  the  stratum  of  denser  air  between 
acting  like  the  glass  of  a  Leyden  jar  in  keeping  the 
opposite  charges  separate.  If  we  could  measure  the 
electric  potential  at  different  points  within  the  thickness 

T 


ELECTRICITY   AND   MAGNETISM      PART  n 

of  the  glass  of  a  charged  jar,  we  should  find  that  the 
values  of  the  potential  changed  in  regular  order  from  a 
4-  value  at  one  side  to  a  —  value  at  the  other,  there  being 
a  point  of  zero  potential  about  half  way  between  the  two. 
Now,  the  air  in  fine  weather  always  gives  +  indications, 
and  the  potential  of  it  is  higher  the  higher  we  go  to 
measure  it.  Cavallo  found  higher  electrification  just 
outside  the  cupola  of  St.  Paul's  Cathedral  than  at  a  lower 
point  of  the  building.  Lord  Kelvin  found  the  potential 
in  the  island  of  Arran  to  increase  from  23  to  46  volts 
for  a  rise  of  one  foot  in  level;  but  the  difference  of 
potential  was  sometimes  eight  or  ten  times  as  much  for 
the  same  difference  of  level,  and  changed  rapidly,  as  the 
east  wind  blew  masses  of  cloud  charged  with  +  or  — 
electricity  across  the  sky.  Joule  and  Kelvin,  at  Aber- 
deen, found  the  rise  of  potential  to  be  equal  to  40  volts 
per  foot,  or  1-3  volts  per  centimetre  rise  of  level. 

During  fine  weather  a  negative  electrification  of  the 
air  is  extremely  rare.  Beccaria  only  observed  it  six 
times  in  fifteen  years,  and  then  with  accompanying 
winds.  But  in  broken  weather  and  during  rain  it  is 
more  often  —  than  +,  and  exhibits  great  fluctuations, 
changing  from  —  to  +,  and  back,  several  times  in  half 
an  hour.  A  definite  change  in  the  electrical  conditions 
usually  accompanies  a  change  of  weather.  "  If,  when 
the  rain  has  ceased  (said  Ceca),  a  strong  excessive  (  +  ) 
electricity  obtains,  it  is  a  sign  that  the  weather  will 
continue  fair  for  several  days." 

334.  Methods  of  Observation.  —  The  older  observers 
were  content  to  affix  to  an  electroscope  (with  gold 
leaves  or  pith-balls)  an  insulated  pointed  rod  stretch- 
ing out  into  the  air  above  the  ground,  or  to  fly  a  kite, 
or  (as  Becquerel  did)  to  shoot  into  the  air  an  arrow  com- 
municating with  an  electroscope  by  a  fine  wire,  which 
was  removed  before  it  fell.  Gay  Lussac  and  Biot  lowered 
a  wire  from  a  balloon,  and  found  a  difference  of  potential 
between  the  upper  and  lower  strata  of  the  air.  None 


CHAP,  iv        ATMOSPHERIC   ELECTRICITY  323 

of  these  methods  is  quite  satisfactory,  for  they  do  not 
indicate  the  potential  at  any  one  point.  To  bring  the 
tip  of  a  rod  to  the  same  potential  as  the  surrounding  air, 
it  is  necessary  that  material  particles  should  be  dis- 
charged from  that  point  for  a  short  time,  each  particle 
as  it  breaks  away  carrying  with  it  a  +  or  a  —  charge 
until  the  potentials  are  equalized  between  the  rod  and 
the  air  at  that  point.  Volta  did  this  by  means  of  a  small 
flame  at  the  end  of  an  exploring  rod.  Lord  Kelvin  has 
employed  a  "  water-dropper,"  an  insulated  cistern  pro- 
vided with  a  nozzle  protruding  into  the  air,  from  whicft 
drops  issue  to  equalize  the  potentials :  in  winter  he  uses 
a  small  roll  of  smouldering  touch-paper.  Dellmann 
adopted  another  method,  exposing  a  sphere  to  influence 
by  the  air,  and  then  insulating  it,  and  bringing  it  within- 
doors to  examine  its  charge.  Peltier  adopted  the  kin- 
dred expedient  of  placing,  on  or  near  the  ground,  a 
delicate  repulsion-electrometer,  which  during  exposure 
was  connected  to  the  ground,  then  insulated,  then  re- 
moved indoors  for  examination.  This  process  really 
amounted  to  charging  the  electrometer  by  influence  with 
electrification  of  opposite  sign  to  that  of  the  air.  The 
"  quadrant "  electrometer,  described  in  Art.  288,  and  a 
"portable"  electrometer  on  the  attracted-disk  principle, 
are  now  used  for  observations  on  atmospheric  electricity. 
Using  a  water-dropping  collector  and  a  Kelvin  electro- 
meter, Everett  made  a  series  of  observations  in  Nova 
Scotia,  and  found  the  highest  +  electrification  in  frosty 
weather,  with  a  dry  wind  charged  with  particles  of  ice. 

335.  Diurnal  Variations.  —  Quetelet  found  that  at 
Brussels  the  daily  indications  (during  fine  weather) 
showed  two  maxima  occurring  in  summer  at  8  A.M.  and. 
9  P.M.,  and  in  winter  at  10  A.M.  and  6  P.M.  respectively, 
and  two  minima  which  in  summer  were  at  the  hours  of 
3  P.M.  and  about  midnight.  He  also  found  that  in  Janu- 
ary the  electricity  was  about  thirteen  times  as  strong  as 
in  June.  At  Kew  there  is  a  maximum  at  8  A.M.  in 


324  ELECTRICITY   AND   MAGNETISM      PAKT  IT 


summer,  and  at  10  A.M.  in  winter;  and  a  second  mini- 
mum at  10  P.M.  in  summer  and  7  P.M.  in  winter.  The 
maxima  correspond  fairly  with  hours  of  changing  tem- 
perature, the  minima  with  those  of  constant  temperature. 
In  Paris,  M.  Mascart  finds  but  one  maximum,  just  before 
midnight :  at  sunrise  the  electricity  diminishes  until  about 
3  P.M.,  when  it  has  reached  a  minimum,  whence  it  rises  till 
nightfall. 

Our  knowledge  of  this  important  subject  is  still  very 
imperfect.  We  do  not  even  know  whether  all  the 
changes  of  the  earth's  electrification  relatively  to  the  air 
are  due  to  causes  operating  above  or  below  the  earth's 
surface.  Simultaneous  observations  at  different  places 
and  at  different  levels  are  greatly  wanted. 

336.  The  Aurora. — In  all  the  northern  regions  of 
the  earth  the  Aurora  borealis,  or  "Northern  Lights,"  is 
an  occasional  phenomenon ;  and  within  and  near  the 
Arctic  circle  is  of  almost  nightly  occurrence.  Similar 
lights  are  seen  in  the  south  polar  regions  of  the  earth, 
and  are  denominated  Aurora  australis.  As  seen  in 
European  latitudes,  the  usual  form  assumed  by  the 
aurora  is  that  of  a  number  of  ill-defined  streaks  or 
streamers  of  a  pale  tint  (sometimes  tinged  with  red  and 
other  colours),  either  radiating  in  a  fan-like  form  from 
the  horizon  in  the  direction  of  the  (magnetic)  north,  or 
forming  a  sort  of  arch  across  that  region  of  the  sky, 
of  the  general  form  shown  in  Fig.  109.  A  certain  nick- 
ering or  streaming  motion  is  often  discernible  in  the 
streaks.  Under  very  favourable  circumstances  the  au- 
rora extends  over  the  entire  sky.  The  appearance  of 
an  aurora  is  usually  accompanied  by  a  magnetic  storm 
(Art.  159),  affecting  the  compass-needles  over  whole 
regions  of  the  globe.  This  fact,  and  the  position  of  the 
auroral  arches  and  streamers  with  respect  to  the 
magnetic  meridian,  directly  suggest  an  electric  origin 
for  the  light,  —  a  conjecture  which  is  confirmed  by  the 
many  analogies  found  between  auroral  phenomena  and 


THE   AURORA 


325 


those  of  discharge  in  rarefied  air  (Arts.  320  and  322). 
Yet  the  presence  of  an  aurora  does  not,  at  least  in  our 
latitudes,  affect  the  electrical  conditions  of  the  lower 
regions  of  the  atmosphere.  On  September  1,  1859,  a 
severe  magnetic  storm  occurred,  and  aurora  were 
observed  almost  all  over  the  globe;  at  the  same  time 


Fig.  169. 

a  remarkable  outburst  of  energy  took  place  in  the 
photosphere  of  the  sun;  but  no  simultaneous  develop- 
ment of  atmospheric  electricity  was  recorded.  Aurorse 
appear  in  greater  frequency  in  periods  of  about  11 J- 
years,  which  agrees  pretty  well  with  the  cycles  of 
maximum  of  magnetic  storms  (see  Art.  159)  and  of 
sun-spots. 


323  ELECTRICITY   AND   MAGNETISM      PART  n 

The  spectroscope  shows  the  auroral  light  to  be  due 
to  gaseous  matter,  its  spectrum  consisting  of  a  few  bright 
lines  not  referable  with  certainty  to  any  known  terrestrial 
substance,  but  having  a  general  resemblance  to  those 
seen  in  the  spectrum  of  the  electric  discharge  through 
rarefied  dry  air. 

The  most  probable  theory  of  the  aurora  is  that  origi- 
nally due  to  Franklin ;  namely,  that  it  is  due  to  electric 
discharges  in  the  upper  air,  in  consequence  of  the  differ- 
ing electrical  conditions  between  the  cold  air  of  the  polar 
regions  and  the  warmer  streams  of  air  and  vapour  raised 
from  the  level  of  the  ocean  in  tropical  regions  by  the 
heat  of  the  sun. 

According  to  Nordenskiold  the  terrestrial  globe  is 
perpetually  surrounded  at  the  poles  with  a  ring  or  crown 
of  light,  single  or  double,  to  which  he  gives  the  name  of 
the  "  aurora-glory."  The  outer  edge  of  this  ring  he  esti- 
mates to  be  at  120  miles  above  the  earth's  surface,  and 
its  diameter  about  1250  miles.  The  centre  of  the  aurora- 
glory  is  not  quite  at  the  magnetic  pole,  being  in  lat.  81° 
1ST.,  long.  80°  E.  This  aurora-glory  usually  appears  as  a 
pale  arc  of  light  across  the  sky,  and  is  destitute  of  the 
radiating  streaks  shown  in  Fig.  169,  except  during 
magnetic  and  auroral  storms. 

An  artificial  aurora  has  bee'n  produced  by  Lemstrom, 
who  erected  on  a  mountain  in  Lapland  a  network  of 
wires  presenting  many  points  to  the  sky.  By  insulating 
this  apparatus  and  connecting  it  by  a  telegraph-wire  with 
a  galvanometer  at  the  bottom  of  the  mountain,  he  was 
able  to  observe  actual  currents  of  electricity  when  the 
auroral  beam  rose  above  the  mountain. 


CHAPTER  V 

ELECTROMAGNETICS 

LESSON  XX VI.  —  Magnetic  Potential 

337.  Electromagnetics.  —  That  branch  of  the  science 
of  electricity  which  treats  of  the  relation  between  elec- 
tric currents  and  magnetism  is  termed  Electromagnetics. 
In  Arts.  128  to  140  the  laws  of  magnetic  forces  were 
explained,  and  the  definition  of  "  unit  pole  "  was  given. 
It  is,  however,  much  more  convenient,  for  the  purpose  of 
study,  to  express  the  interaction  of  magnetic  and  electro- 
magnetic systems  in  terms  not  of  "force"  but  of  "poten- 
tial" ;  i.e.  in  terms  of  their  power  to  do  work.  In  Art. 
263  the  student  was  shown  how  the  electric  potential  due 
to  a  quantity  of  electricity  may  be  evaluated  in  terms  of 
the  work  done  in  bringing  up  as  a  test  charge  a  unit  of 
-f  electricity  from  an  infinite  distance.  Magnetic  poten- 
tial can  be  measured  similarly  by  the  ideal  process  of 
bringing  up  a  unit  magnetic  pole  (N-seeking)  from  an 
infinite  distance,  and  ascertaining  the  amount  of  work 
done  in  the  operation.  Hence  a  large  number  of  the 
points  proved  in  Lesson  XXI.  concerning  electric  poten- 
tial will  also  hold  true  for  magnetic  potential.  The 
student  may  compare  the  following  propositions  with  the 
corresponding  ones  in  Articles  263  to  268:  — 

(a)   The  magnetic  potential  at  any  point  is  the  work  that 
must   be   spent  upon  a  unit   magnetic   (N-seeking) 
327 


328  ELECTRICITY  AND   MAGNETISM      PART  n 

pole  in  bringing  it  up  to  that  point  from  an  infinite 
distance. 

(b)  The  magnetic  potential  at  any  point  due  to  a  system 
of  magnetic  poles  is  the  sum  of  the  separate  magnetic 
potentials  due  to  the  separate  poles. 

The  student  must  here  remember  that  the  potentials 
due  to  S-seeking  poles  will  be  of  opposite  sign  to  those 
due  to  N-seeking  poles,  and  must  be  reckoned  as  negative. 

(c)  The  (magnetic)  potential  at  any  point  due  to  a  system 
of  magnetic  poles  may  be  calculated  (compare  with 
Art.  263)  by  summing  up  the  strengths  of  the  sep- 
arate poles  divided  each  by  its  own  distance  from 
that  point.     Thus,  if   poles  of   strengths  m',  m1', 
m'",  etc.,  be  respectively  at  distances  of  r',  r",  r'", 
.     .     .     from  a  point  P,  then  the  following  equa- 
tion gives  the  potential  at  P  :  — 


or      F  =         - 

r 

(d)  The  difference  of  (magnetic)  potential  between  two 
points   is   the   work   to   be   done   on    or   by    a   unit 
(N-seeking)  pole  in  moving  it  from  one  point  to  the 
other.     It  follows  that  if   m  units  of   magnetism 
are  moved  through  a  difference  of  potential  V,  the 
work  W  done  will  be 

W  =  roV. 

(e)  Magnetic  force  on  unit  pole  is  the  rate  of  change 
of  (magnetic)   potential  per  unit   of  length  :   it  is 
numerically  equal   to  the  intensity  of   the  field. 
Since  by  Art.  141, 


and  work  is  the  product  of  a  force  into  the  length 


CHAP,  v  MAGNETIC   POTENTIAL  329 

through  which  its  point  of  application  moves  for- 
ward, it  follows  that 


But 

W  =  mV; 

whence 

V  =  RI, 

and 

H  =  V//. 

Example.  —  The  difference  of  magnetic  potential  between  two 
points  5  centims.  apart  along  a  magnetic  field  in  which  there 
are  GOOD  lines  per  sq.  cm.,  is  30,000.  Or,  it  would  require 
30,000  ergs  of  work  to  be  expended  to  push  a  unit  pole  from 
one  point  to  the  other  against  the  magnetic  force. 

(f)  Equipotential  surfaces  are  those  (imaginary}  surfaces 
surrounding  a  magnetic  pole  or  system  of  poles,  over 
which  the  (magnetic}  potential  has  equal  values. 
Thus,  around  a  single  isolated  magnetic  pole,  the 
potential  would  be  equal  all  round  at  equal  dis- 
tances ;  and  the  equipotential  surfaces  would  be 
a  system  of  concentric  spheres  at  such  distances 
apart  that  it  would  require  the  expenditure  of  one 
erg  of  work  to  move  a  unit  pole  up  from  a  point 
on  the  surface  of  one  sphere  to  any  point  on  the 
next  (see  Fig.  146).  Around  any  real  magnet 
possessing  two  polar  regions  the  equipotential  sur- 
faces would  be  much  more  complicated.  Magnetic 
force,  whether  of  attraction  or  repulsion,  always  acts 
across  the  equipotential  surfaces  in  a  direction  nor- 
mal to  the  surface;  the  magnetic  lines  of  force  are 
everywhere  perpendicular  to  the  equipotential  sur- 
faces. 

Flux  of  Force.  —  From  a  single  magnetic  pole  (sup- 
posed to  be  a  point  far  removed  from  all  other  poles)  the 
lines  of  force  diverge  radially  in  all  directions.  The 
space  around  may  be  conceived  as  thus  divided  up  into 


330  ELECTRICITY  AND  MAGNETISM       PART  n 

a  number  of  conical  regions,  each  having  their  apex  at 
that  pole ;  and  through  each  cone,  as  through  a  tube, 
a  certain  number  of  lines  of  force  will  pass.  Such  a 
conical  space  may  be  called  a  "  tube "  of  force.  The 
total  number  of  magnetic  lines  within  any  tube  of  force 
is  called  the  magnetic  flux.*  No  matter  where  you  cut 
across  a  tube  of  force,  the  cross-section  will  cut  through 
the  enclosed  flux,  though  the  lines  diverge  more  widely 
as  the  tube  widens.  Hence, 

(g)  The  magnetic  flux  across  any  section  of  a  tube  of 
force  is  constant  wherever  the  section  be  taken. 

In  case  the  magnetism  is  not  concentrated  at  one 
point,  but  distributed  over  a  surface  from  which  the 
tubes  start,  we  shall  have  to  speak  of  the  "  amount  of 
magnetism"  rather  than  of  the  "strength  of  pole,"  and 
in  such  a  case  the 

(h)  Magnetic  density  is  the  amount  of  magnetism  per 
unit  of  surface.  In  the  case  of  a  simple  magnetic 
shell  over  the  face  of  which  the  magnetism  is 
distributed  with  uniform  density,  the  "  strength  " 
of  the  shell  will  be  equal  to  the  thickness  of 
the  shell  multiplied  by  the  surface-density. 

338.  Intensity  of  Field. —  We  have  seen  (Art.  115) 
that  every  magnet  is  surrounded  by  a  certain  "field," 
within  which  magnetic  force  is  observable.  We  may 
completely  specify  the  properties  of  the  field  at  any 
point  by  measuring  the  strength  and  the  direction  of  that 
force,  —  that  is,  by  measuring  the  "  intensity  of  the  field  " 
and  the  direction  of  the  lines  of  force.  The  "  intensity  of 
the  field  "  at  any  point  is  measured  by  the  force  with  which 
it  acts  on  a  unit  pole  placed  at  that  point.  Hence,  unit 
intensity  of  field  is  that  intensity  of  field  which  acts  on  a  unit 
pole  with  a  force  of  one  dyne.  There  is  therefore  a  field  of 

*  The  magnetic  flux  is  by  some  writers  called  the  total  induction ; 
but  the  word  induction  ought  to  be  kept  for  the  operation  of  inducing. 


CHAP,  v         LINES   IN  MAGNETIC   FIELD  331 

unit  intensity  at  a  point  one  centimetre  distant  from  the 
pole  of  a  magnet  of  unit  strength.  Suppose  a  magnet 
pole,  whose  strength  is  ?/*,  placed  in  a  field  at  a  point 
where  the  intensity  is  H,  then  the  force  will  be  in  times 
as  great  as  if  the  pole  were  of  unit  strength,  and 

f=m  x  H. 

To  aid  the  imagination  by  a  graphic  conception  we 
adopt  Faraday's  notion  of  representing  the  properties  of  a 
magnetic  field  by  supposing  lines  to  be  drawn  so  that 
they  represent  the  direction  and  intensity  of  the  field  by 
the  direction  and  density  of  the  lines.  This  leads  to  the 
empirical  rule  to  draw  as  many  magnetic  lines  to  the 
square  centimetre  (of  cross  section)  as  there  would  be 
dynes  of  force  on  unit  pole.  A  field  of  H  units  means 
one  where  there  would  be  H  dynes  on  unit  pole,  or  H 
lines  per  square  centimetre.  It  follows  that  a  unit  mag- 
netic pole  will  have  4?r  lines  of  force  proceeding  from  it:  for 
there  is  unit  field  at  unit  distance  away,  or  one  magnetic 
line  per  square  centimetre ;  and  there  are  4rr  square 
centimetres  of  surface  on  a  sphere  of  unit  radius  drawn 
round  the  pole.  A  magnet,  whose  pole-strength  is  m,  has 
4i7rm,  or  12-57  x  m,  lines  running  through  the  steel,  and 
diverging  at  its  pole.  The  above-mentioned  rule  is  the 
origin  of  the  4?r  symbol  which  comes  in  so  often  into 
electromagnetic  formulae.  Suppose  a  narrow  crevasse 
between  the  faces  of  two  opposing  magnets,  each  having  <r 
units  of  magnetism  per  square  centimetre  of  their  pole 
surfaces.  The  field  in  the  space  between  will  have  the 
value 

H  =  47TO-. 

339.  Work  done  by  Conductor  carrying  Current 
when  it  cuts  across  the  Lines  of  a  Magnetic  Field.— 
By  definition  (Art.  263)  it  follows  that  the  work  W 
done  in  moving  Q  units  of  electricity  against  an  electro- 
motive-force V  is  equal  to  QV.  Suppose  that  this  electro- 


ELECTRICITY   AND   MAGNETISM      PART  n 

motive-force  is  due  to  the  conductor  cutting  N  magnetic 
lines  during  time  t.  Then  if  the  motion  be  uniform  and 
the  average  current  during  the  time  is  called  C,  it  follows 
that  Q  =  Ct.  And  the  average  electromotive-force  is  (see 
Art.  225)  =  N/£.  Inserting  these  values  we  get 

W  =  Ct  x  N/f, 
or  W  =  CN; 

or,  in  words,  the  work  done  in  moving  a  current  across  a 
magnetic  flux  is  equal  to  the  product  of  the  current  into  the 
total  number  of  magnetic  lines  cut.  It  will  be  noted  that 
the  work  is  the  same  whether  the  time  is  long  or  short. 
If  C  and  N  are  in  absolute  (C.G.S.)  units,  W  will  be  in 
ergs. 

34O.  Force  exerted  by  Magnetic  Field  on  Wire  carry- 
ing Current.  —  If  a  wire  is  moved  sideways  across  the 
lines  of  a  magnetic  field,  through  a  distance  x  it  will 
sweep  out  an  area  equal  to  its  own  length  I  multiplied 
by  x.  And  if  H  is  the  number  of  magnetic  lines  per 
square  centimetre  the  total  number  of  lines  cut  will  be 
=  Elx ;  and  the  work  done  if  the  wire  carries  current 
C  will  be  =  CH/x.  But  if  work  W  is  done  in  moving  the 
wire  through  distance  x  the  force  /  exerted  will  be  W/x. 
Hence  the  force  on  the  wire  will  be 

/=CHJ; 

or,  in  words,  the  force  is  proportional  to  the  current,  to 
the  intensity  of  the  field,  and  to  the  length  of  wire  in  the 
field.  It  is  a  force  that  tends  to  drag  the  wire  laterally, 
acting  at  right  angles  to  the  wire  and  to  the  lines  of  the 
field. 

This  action  is  of  course  due  to  stresses  going  on  in  the 
medium,  and  is  worthy  of  further  thought.  Consider 
the  magnetic  field  in  a  gap  between  a  large  N-pole  and 
a  similar  S-pole.  The  lines  will  go  nearly  uniformly 
straight  across.  Let  a  current  flow  in  a  copper  wire  that 
lies  across  the  field.  In  Fig.  170  the  wire  is  seen  end- 


MAGNETOMOTIVE    FORCE 


333 


ways,  with   the   current   flowing   "  up "   or   toward   the 

observer.     The  result  will  be  that  the  magnetic  field  of 

the  current  (Art.  202)  will  be  superposed  upon  that  of 

the  magnets,  and  will 

perturb   it :    the  form 

of  the  perturbed  field 

being  that  shown.     In 

such  a  field  the  stresses, 

which   act   as  though 

the      magnetic      lines 

tended       to      shorten 

themselves,  will    have 

the  effect  of  urging  the 

wire    mechanically   in 

the   direction    shown. 

This  mechanical  force 

acts  on  the  matter  of 

the  wire,  though    due 

to  the  current. 

In   calculating   by 
the  expression  above,  if  C  is  given  in  amperes  it  must  be 
divided  by  10. 

341.  Magnetomotive-force  (or  Total  Magnetizing 
Force)  of  a  Current  circulating  in  a  Spiral  Conductor.  — 
Let  a  conductor  carrying  a  current  of  C  amperes  be  coiled 
up  in  a  spiral  having  S  as  the  number  of  turns.  It  is 
known,  and  easily  understood,  that  the  total  magnetizing 
force  of  such  is  proportional  to  the  number  of  ampere- 
turns;  for  experiment  shows  that,  for  example,  a  current 
of  10  amperes  circulating  in  a  coil  of  50  turns  has  pre- 
cisely the  same  magnetic  power  as  a  current  of  5  amperes 
in  100  turns,  or  as  a  current  of  1  ampere  in  500  turns. 
Each  of  these  has  500  ampere-turns. 

To  obtain  the  full  expression  let  us  find  the  work  that 
would  be  done  in  the  act  of  moving  a  unit  magnet-pole 
around  any  closed  path  (Fig.  171)  from  any  point  P  to 
the  same  point  again,  such  path  passing  through  all  the 


Fig.  170. 


334  ELECTRICITY   AND   MAGNETISM       PART  n 

turns  of  the  magnetizing  coil.  The  work  done  on  a  unit 
pole  in  moving  it  once  around  the  closed  path,  against 
the  magnetic  forces  of  the  system,  is  a  measure  of  the 
power  of  that  system  to  magnetize:  or,  in  other  words,  is  a 
measure  of  its  magnetomotive-force.  Such  a  closed  path 
may  lie,  according  to  circumstances,  either  wholly  in  air, 
or  partly  in  air  partly  in  iron,  or  wholly 
in  iron.  The  argument  is  entirely  in- 
dependent of  any  materials  lying  along 
'v._  _.,.-''  the  ideal  path. 

Fig.  171.  Now  imagine  this  unit-pole,  with  its 

4?r  magnetic  lines  radiating  out  of  it,  to 
be  passed  along  the  closed  path  (Fig.  171)  from  P,  through 
the  spirals  to  P  again.  Each  turn  of  the  coil  will  cut  each 
of  the  magnetic  lines  once,  and  therefore,  by  Arts.  338 
and  339,  the  total  work  done  will  be 

W  =  47rCS/10, 

where  we  divide  by  10  to  bring  amperes  to  C.G.S.  units. 
Or,  since  4?r  =  12-57,  we  get  the  rule — the  magnetomotive- 
force*  of  a  coil  is  equal  to  1-257  times  the  ampere-turns. 

342.  Intensity  of  Field  in  a  Long  Tubular  Coil,  or 
Solenoid.  —  A  spiral  coil  wound  on  a  tube  is  called  a 
solenoid.  It  has,  when  a  current  circulates  in  its  coils, 
a  magnetic  field  along  the  inside  of  it,  and  is,  in 
fact,  so  long  as  the  current  circulates,  a  magnet  without 
iron.  This  magnetic  field,  if  the  spiral  is  a  very  long  one 
—  say  20  times  as  long  as  the  diameter  of  the  spirals,  — 
is  very  uniform  all  along  the  interior,  except  just  toward 
the  ends,  where  it  becomes  weaker.  To  find  the  intensity 
of  the  field  H,  we  may  remember  that  (Art.  337  e)  the 
work  done  on  a  unit-pole  in  moving  it  through  a  length 
I  of  field  H  is  equal  to  H/.  But  the  work  done  in 

*  Since  this  magnetomotive-force  is  made  up  of  a  number  of  small 
elements  distributed  variously  along  the  path  it  is  sometimes  called  tho 
line-integral  of  the  magnetizing  forces. 


FIELD   DUE   TO    CURRENT  335 


moving  it  along  the  tubular  coil  of  length  I  is  practically 
equal  to  that  done  around  the  closed  path,  since  nearly 
all  the  forces  are  met  along  the  part  of  the  path  inside. 
Hence  we  may  equate  47rCS/10  to  H/;  giving  the  result 


, 

10        / 

or  the  intensity  of  the  field  in  a  long  spiral  is  equal  to  1-257 
times  the  number  of  ampere-turns  per  centimetre  of  length. 

At  the  mouth  of  a  long  spiral  the  intensity  of  the  field 
is  exactly  half  what  it  is  midway  between  the  ends. 

343.  Magnetic  Field  due  to  Indefinitely  Long  Straight 
Current.     Law  of  Inverse  Simple  Distance.  —  Consider  a 
unit-pole   at  point  P  at  a  distance  r  (Fig. 
172)  from  an  indefinitely  long  straight  con- 
ductor   carrying    a    current    of    C    amperes. 
The  force  tending  to  make  the  pole  circulate 
around  the  wire  may  be  calculated  very  sim- 
ply as  follows.     If  the  unit-pole  were  to  be 
moved  once  around  the  wire  on  a  circular 
path  with  radius  r,  each  one  of  the  4?r  mag- 
netic lines  that  radiate  from  it  would  be  cut 
once  by  the  wire.      Hence,  by  Art.  339,  the 
work  done  in  one  such  revolution  would  be       Fi»'  172- 
equal  to  47rC/10.     But  this  work  has  been  done  by  mov- 
ing the  unit,  against  the  forces  of  the  system,  along  a 
path  the  length  of  which  is  27rr;  wherefore 

W  =/x  2irr  =  47rC/10, 
whence 

/=2C/10r. 

From  this  it  appears  that  the  force  on  unit-pole,  and 
therefore  the  intensity  of  the  field,  is  directly  proportional 
to  the  current,  and  varies  inversely  as  the  simple  distance 
from  the  wire. 

Example.  —  The  force  exerted  on  a  pole  of  1200  units  of 


ELECTRICITY   AND   MAGNETISM       PART  11 


magnetism  at  a  distance  of  4  centimetres  from  a  long 
straight  wire  carrying  current  of  60  amperes  will  be  3600 
dynes,  or  3'52  grammes. 

The  fact  that  the  force  varies  inversely  as  the  simple 
distance,  and  not  as  the  square,  was  experimentally 
discovered  by  Biot  and  Savart  in  1820. 

Around  such  a  straight  conductor  the  magnetic  field 
consists  of  a  cylindrical  whirl  of  circular  lines  (Art.  202), 
their  density  decreasing  as  their  radius  increases.  Outside 
a  straight  wire  carrying  a  10  ampere  current  the  values  of 
Hare:  2  at  1  cm.;  1  at  2  cm.;  0*4  at  5  cm.,  and  so 
forth.  The  pole  tends  to  move  circularly  around  the 
wire. 

344.    Mutual  Action  of  Magnet-pole  and  of  Element 
of  Current.  —  Consider  an  element  of  current,  that  is  to 
say,  an  indefinitely  short  piece 
I          of  a  conductor  traversed  by  a 
current.     Calling  the  length  dl, 
and  the  current  C,  we  have  Cell 
as   the   magnetic   value  of  the 
|          element    with    respect    to    all 
Fig.  173.  points    in    its  equatorial  plan. 

Suppose  the  element  to  be  set 

(Fig.  173)  at  distance  r  from  a  magnet-pole  of  m  units, 
and  at  right  angles  to  the  line  joining  them.  Then, 
as  the  element  is  small  compared  with  r,  the  law  of 
inverse  squares  will  hold  good:  the  mutual  force  will  be 

-_ 


10-r2 

This  will  be  neither  an  attraction  nor  a  repulsion,  but  a 
force  at  right  angles  to  the  element  and  to  the  line  join- 
ing it  to  in. 

345.  Magnetic  Field  due  to  Circular  Current.  —  Tt 
is  desired  to  find  the  effect  of  a  circular  current  (Fig. 
174)  at  any  point  on  the  axis,  at  a  distance  x  from  the 
centre.  Suppose  a  unit-pole  were  placed  at  this  point 


CHAP,  v          FIELD   OF   CIRCULAR   COIL  337 

P,  only  a  fraction  of  the  4?r  lines  which  radiate  from  it 

will  pass  through  the  circle  ;  the  number  being  propor- 

tional to  the   solid-angle    (Art.  148)  , 

subtended  at  P  by  the  circle,  namely 

27r  (1  -  cos  0),  where  0  is  the   angle   /JY^^L        !/ 

between    axis  and  slant   distance    a.  \   \  \        v^y 

Hence  in  bringing  up  the  pole  to  this 

place,  from   an   infinite  distance,  the 

work  done  by  causing  these  lines  to  Fig.  174. 

cut  across  the  wire  carrying  current  C  amperes  will  be 

(by  Art.  339) 

W  =  27rC(l  -cos0)/10. 

This  represents  the  mutual  energy  of  pole  and  current. 
To  calculate  the  force  at  P  we  must  differentiate  this 
expression  with  respect  to  x,  to  ascertain  the  rate  at  which 
the  mutual  energy  falls  per  unit  length.  For  this  purpose 
it  will  be  convenient  to  substitute  for  cos  0  its  value 

x/(x'2  -f  y2)^.     Substituting  and  differentiating  we  get 
/=  dW/dx  = 


Now  (#2  +  i/2)^  is  equal  to  a3  ;  whence  the  rule  that  the 
magnetic  force  at  any  point  P  on  the  axis  varies  directly 
as  the  current,  and  inversely  as  the  cube  of  the  slant  distance. 
(Compare  case  of  a  bar-magnet,  Art.  138.) 

Another  way  of  arriving  at  this  result  is  as  follows. 
Taking  the  expression  found  in  Art.  344  for  the  action  of 
an  element  of  current,  we  may  consider  the  effect  of  the 
topmost  element  of  the  ring  (Fig.  174),  situated  at  a 
slant  distance  a  =  Vx2  +  y2.  The  elementary  force  df 
exerted  on  unit-pole  at  P  by  the  element  Cdl  will  be  at 
right  angles  to  a  and  to  dl  (in  direction  of  the  arrow), 
and,  by  Art.  206,  of  the  value 


As  the  elements  such  as  dl  are  symmetrical  around  the 
axis  we  must  resolve  their  oblique  forces  into  two  parts  ; 
z 


ELECTRICITY   AND    MAGNETISM      PART  n 

part  acting  at  right  angles  to  the  axis,  which  will  dis- 
appear by  mutually  cancelling  out  in  pairs,  and  part 
acting  in  the  line  of  the  axis,  which  will  for  each  element 
be  equal  to  the  above  expression  multiplied  by  sin  0~  So 
that  the  elementary  axial  force  due  to  each  element  of 
length  dl  will  be 

rf/=C^-sin0/ioa2; 

or,  since  sin  0  =  y/a, 

df=  Cdl-yoi/  a8. 

But  the  total  force  /  due  to  all  the  elements  will  be  the 
integral  due  to  the  sum  of  their  lengths,  and  this  integral 
length  around  the  circle  isfdl  =  2-iry.  Whence  it  at  once 
follows  that 


Note  that  if  P  is  pushed  up  to  the  centre  of  the  circle 
a  =  y,  and  we  get  back  to  the  rule  for  tangent  galva- 
nometer (Art.  212),  /  =  27rC/ior. 

Also  note  that  for  very  great  distances  of  P  from 
centre  a  becomes  sensibly  equal  to  x,  the  force  varying 
inversely  as  the  cube  of  the  axial  distance. 

This  affords  one  way  of  varying  the  sensitiveness  of 
tangent  galvanometers,  the  needle  with  its  scale  being 
arranged  to  slide  out  along  the  axis  of  the  coil.  At  a 
point  P,  such  that  a  =  2y,  the  force  of  coil  on  needle  is 
only  J  of  what  it  is  at  centre. 

346.  Moment  of  Circular  Coil.  —  A  circular  coil  carry- 
ing a  current  acts  as  a  magnet  whose  axis  is  the  axis 
of  the  coil.  Its  magnetic  moment  (Art.  135)  will  be  the 
product  of  the  current  (in  absolute  units)  into  the  area 
enclosed.  Or,  if  C  is  in  amperes,  and  A  the  total  area 
of  all  the  turns,  its  moment  will  be  AC/  10.  If  such  a 
coil  is  placed  in  a  field  of  intensity  H  it  will  tend  to 
turn  so  as  to  place  its  axis  along  the  direction  of  the  field. 
If  the  angle  between  those  directions  is  0  the  torque  (or 
turning-moment)  will  be  =  ACH  sin  0/10. 


CHAP,  v     POTENTIAL   OF   MAGNETIC   SHELL 


347.  Potential  due  to  a  Solenoidal  or  Circuital  Distribution 
of  Magnetism.  —  A  long  thin  uniformly  magnetized  magnet 
exhibits  poles  only  at  the  two  ends,  and  acts  on  external  objects 
just  as  if  there  were  two  equal  quantities  of  opposite  kinds  of 
magnetism  collected  at  these  two  points.  Such  a  distribution 
of  magnetism  is  sometimes  called  solenoidal  or  circuital.  The 
magnetic  potential  due  to  a  solenoid,  and  all  its  magnetic 
effects,  depend  only  on  the  position  of  its  two  poles,  and  on 
their  strength,  and  not  on  the  form  of  the  bar  between  them, 
whether  straight  or  curved.  In  Art.  337  (c)  was  given  the  rule 
for  finding  the  potential  due  to  a  system  of  poles.  Suppose  the 
two  poles  of  a  solenoid  have  strengths  +  m  and  —  m  respectively, 
and  that  the  distances  of  these  poles  from  an  external  point  P 
are  r-±  and  r2,  then  the  potential  at  P  will  be 

v,-»(i-± 


Suppose  a  magnet  curled  round  until  its  N  and  S  poles  touch 
one  another  :  it  will  not  act  as  a  magnet  on  an  external  object, 
and  will  have  no  "  field  "  ;  for  if  the  two  poles  are  in  contact, 
their  distances  r±  and  r2  to  an  external  point  P  will  be  equal,  and 


f!—  !\wfllbe  = 

VTi     ?'2/ 


348.  Potential  due  to  a  Magnetic  Shell.  —  Gauss  demon- 
strated that  the  potential  due  to  a  magnetic  shell  at  a  point  near 
it  is  equal  to  the  strength  of  the  shell  multiplied  by  the  solid-angle 
subtended  by  the  shell  at  that  point  ;  the  "  strength  "  of  a  magnetic 
shell  being  the  product  of  its 
thickness  into  its  surface- 
density  of  magnetization. 

If  w  represents  the  solid- 
angle  subtended  at  the  point 
P,  and  i  the  strength  of  the 
shell,  then 

Vp  =wi. 


Fig.  175. 


Proof.  — To  establish  this 
proposition  would  require  the 
integral  calculus.    But  the  following  geometrical  demonstration, 
though  incomplete,  must  here  suffice. 

Let  us  consider  the  shell  as  composed,  like  that  drawn,  of  a 
series  of  small  elements  of  thickness  t,  and  having  each  an  area 
of  surface  s.  The  whole  solid-angle  subtended  at  P  by  the  shell 


340  ELECTRICITY   AND   MAGNETISM      PART  n 


may  likewise  be  conceived  as  made  up  of  a  number  of  elementary 
small  cones,  each  of  solid-angle  «J :  Let  ?\  and  r%  be  the  distances 
from  P  to  the  two  faces  of  the  element :  Let  a  section  be  made 
across  the  small  cone  orthogonally,  or  at  right  angles  to  TI,  and 
call  the  area  of  this  section  a  :  Let  the  angle  between  the  sur- 
faces s  and  a  be  called  angle  £:  then  5  —  a/cos  P.  Let  i  be  the 
"  strength  "  of  the  shell  (i.e.  =  its  surface-density  of  magnetism 
X  its  thickness) ;  then  i/t  =  surface-density  of  magnetism,  and 
si/t  =  strength  of  either  pole  of  the  little  magnet  =  m. 

area  of  its  orthogonal  section 
Now  solid-angle  w  = —• 

=  a/r2  ; 

therefore  a  =  ^>r2, 

and  s  —  wr2/cos  /3. 

Hence          uirt/t  cos  ft  =  m. 

But  the  potential  at  P  of  the  magnet  whose  pole  is  m  will  be 


r& 


t  COS  ft 


1       1      r2—r-i  7*2  —  TI 

but  —  —  ,  which  we  may  write  —  -%  — 

'  1        '2  '  V  2 

because  r\  and  r%  may  be  made  as  nearly  equal  as  we  please. 
And  since  r2  —  TI  =  t  cos  /3 


or  the  potential  due  to  the  element  of  the  shell  =  the  strength 
of  the  shell  X  the  solid-angle  subtended  by  the  element  of  the 
shell.  Hence,  if  V  be  the  sum  of  all  the  values  of  v  for  all  the 
different  elements,  and  if  w  be  the  whole  solid-angle  (the  sum 
of  all  the  small  solid-angles  such  as  <6)  , 

VP  -  «i, 

or  the  potential  due  to  a  magnetic  shell  at  a  point  is  equal  to 
the  strength  of  the  shell  multiplied  by  the  solid-angle  subtended 
by  the  whole  of  the  shell  at  that  point. 

Hence  <»i  represents  the  work  that  would  have  to  be  done  on  or 
by  a  unit-pole,  to  bring  it  up  from  an  infinite  distance  to  the  point 
P,  where  the  shell  subtends  the  solid-angle  w.  At  a  point  Q 


CHAP,  v    POTENTIAL   OF   MAGNETIC   SYSTEM      341 


where  the  solid-angle  subtended  by  the  shell  is  different,  the 
potential  will  be  different,  the  difference  of  potential  between 
P  and  Q  being 

Vv-Vr  =  *(**-"*). 

If  a  magnet-pole  whose  strength  is  m  were  brought  up  to  P, 
m  times  the  work  would  have  to  be  done,  or  the  mutual  poten- 
tial would  be  =  wwz. 

349.  Potential  of  a  Magnet-pole  on  a  Shell.— It  is  evi- 
dent that  if  the  shell  of  strength  i  is  to  be  placed  where  it 
subtends  a  solid-angle  to  at  the  pole  m,  it  would  require  the 
expenditure  of  the  same  amount  of  work  to  bring  up  the  shell 
from  an  infinite  distance  on  the  one  hand,  as  to  bring  up  the 
magnet-pole  from  an  infinite  distance  on  the  other ;  hence  mtai 
represents  both  the  potential  of  the  pole  on  the  shell  and  the 
potential  of  the  shell  on  the  pole.  Now  the  lines  of  force  from  a 
pole  may  be  regarded  as  proportional  in  number  to  the  strength 
of  the  pole,  and  from  a  single  pole  they  would  radiate  out  in  all 
directions  equally.  Therefore,  if  a  magnet-pole  was  placed  at  P, 
at  the  apex  of  the  solid-angle  of  a  cone,  the  number  of  lines  of 
force  which  would  pass  through  the  solid-angle  would  be  propor- 
tional to  that  solid-angle.  It  is  therefore  convenient  to  regard 
mm  as  representing  the  number  of  lilies  of  force  of  the  pole  which 
pass  through  the  shell,  and  we  may  call  the  number  so  inter- 
cepted N.  Hence  the  potential  of  a  magnet-pole  on  a  mag- 
netic shell  is  equal  to  the  strength  of  the  shell  multiplied  by  the 
number  of  lines  of  force  (due  to  the  magnet-pole)  which  pass 
through  the  shell ;  or  V  =  Nz.  If  either  the  shell  or  the  pole 
were  moved  to  a  point  where  a  different  number  of  lines  of  force 
were  cut,  then  the  difference  of  potential  would  be 

VQ-Vr  =  ±i  (NQ-NP). 

To  bring  up  a  N-seeking  (or  +)  pole  against  the  repelling 
force  of  the  N-seeking  face  of  a  magnetic  shell  requires  a  posi- 
tive amount  of  work  to  be  done;  and  their  mutual  reaction 
would  enable  work  to  be  done  afterwards  by  virtue  of  their 
position:  in  this  case  then  the  potential  is  +.  But  in  moving  a 
N-seeking  pole  up  to  the  S-seeking  face  of  a  shell  work  will  be 
done  by  the  pole,  for  it  is  attracted  up;  and  as  work  done  by 
the  pole  may  be  regarded  as  our  doing  negative  work,  the 
potential  here  will  have  a  negative  value. 

Again,  suppose  we  could  bring  up  a  unit  N-seeking  pole 
against  the  repulsion  of  the  N-seeking  face  of  a  shell  of  strength 
i,  and  should  push  it  right  up  to  the  shell  ;  when  it  actually 
reached  the  plane  of  the  shell  the  shell  would  occupy  a  whole 


342  ELECTRICITY   AND   MAGNETISM       PART  n 


horizon,  or  half  the  whole  space  around  the  pole,  the  solid-angle* 
it  subtended  being  therefore  2n-,  and  the  potential  will  be  +  2iri. 
If  we  had  begun  at  the  S-seeking  face  the  potential  at  that  face 
would  be  —  2rri.  It  appears  then  that  the  potential  alters  its 
value  by  &ni  on  passing  from  one  side  of  the  shell  to  the  other. 

There  is  a  reaction  between  pole  and  shell  similar  to  that 
(Art.  121)  between  pole  and  pole. 

If  a  N-seeking  pole  be  brought  up  to  the  N-seeking  face  of  a 
shell  none  of  the  lines  of  force  of  the  magnet  will  cut  the  shell, 
but  will  be  repelled  out  as  in  Fig.  72  ;  whereas  if  a  N-seeking  pole 
be  brought  up  to  the  S-seeking  face  of  a  shell,  large  numbers  of 
the  lines  will  be  run  into  one  another;  and  the  pole,  as  a  matter 
of  fact,  will  be  attracted  up  to  the  shell,  where  as  many  lines  of 
force  as  possible  are  cut  by  the  shell.  We  may  formulate  this 
action  by  saying  that  a  magnetic  shell  and  a  magnet-pole  react 
on  one  another  and  urge  one  another  in  such  a  direction  as 
to  make  the  number  of  lines  of  force  that  are  cut  by  the  shell  a 
maximum  (Maxwell's  Rule,  Art.  204).  Outside  the  attracting 
face  of  the  shell  the  potential  is  —  u>i,  and  the  pole  moves  so  as  to 
make  this  negative  quantity  as  great  as  possible,  or  to  make  the 
potential  a  minimum.  Which  is  but  another  way  of  putting  the 
matter  as  a  particular  case  of  the  general  proposition  that  bodies 
tend  to  move  so  that  the  energy  they  possess  in  virtue  of  their 
position  tends  to  run  down  to  a  minimum. 

35O.  Magnetic  Potential  due  to  Current.  —  The  proposi- 
tions concerning  magnetic  shells  given  in  the  preceding  para- 
graphs derive  their  great  importance  because  of  the  fact  laid 
down  in  Art.  203  that  circuits,  traversed  by  currents  of  electri- 
city, behave  like  magnetic  shells.  Adopting  the  electromagnetic 
unit  of  current  (Art.  353),  we  may  at  once  go  back  to  Art.  347, 
and  take  the  theorems  about  magnetic  shells  as  being  also  true 
of  closed  voltaic  circuits. 

(a)  Potential  due  to  closed  circuit  (compare  Art.  348). 

The  potential  V  due  to  a  closed  voltaic  circuit  (traversed  by 
a  current)  at  a  point  P  near  it,  is  equal  to  the  strength  of  the 
current  multiplied  by  the  solid-angle  u>  subtended  by  the  circuit 
at  that  point.  If  C  be  the  strength  of  the  current  in  electro- 
magnetic units,  then 

(6)  At  a  point  Q,  where  the  solid-angle  subtended  by  the 
circuit  is  WQ  instead  of  t»P,  the  potential  will  have  a  different 
value,  the  difference  of  potential  being 


*  See  note  on  "Ways  of  Reckoning  Angles,  Art.  144  and  Appendix  A. 


CHAP,  v  MUTUAL  POTENTIAL  343 


(c)  Mutual  Potential  of  a  Magnet-pole  and  a  Circuit. —If 
a  magnet-pole  of  strength  m  were  brought  up  to  P,  m  times  as 
much  work  will  be  done  as  if  the  magnet-pole  had  been  of  unit 
strength,  and  the  work  would  be  just  as  great  whether  the  pole 
m  were  brought  up  to  the  circuit,  or  the  circuit  up  to  the  pole. 
Hence,  the  mutual  potential  will  be 

—  WwC. 

1  But,  as  in  Art.  349,  we  may  regard  raw  as  representing  the 
number  of  lines  of  force  of  the  pole  which  are  intercepted  by 
and  pass  through  the  circuit,  and  we  may  write  N  for  that  num- 
ber, and  say 

V  =  -CN, 

or  the  mutual  potential  of  a  magnet-pole  and  a  circuit  is  equal 
to  the  strength  of  the  current  multiplied  by  the  number  of  the 
magnet-pole's  lines  of  force  that  are  intercepted  by  the  circuit, 
taken  with  reversed  sign. 

(d)  As  in  the  case  of  the  magnetic  shell,  so  with  the  circuit, 
the  value  of  the  potential  changes  by  4  nC  from  a  point  on  one 
side  of  the  circuit  to  a  point  just  on  the  other  side;  that  is  to 
say,  being  —2irC  on  one  side  and  +27rC  on  the  other  side  work 
equal  to  4  TrC  must  be  done  in  carrying  a  unit-pole  from  one  side 
to  the  other  round  the  outside  of  the  circuit.    The  work  done  in 
thus  threading  the  circuit  along  a  path  looped  S  times  round  it 
would  be  4  Ti-SC. 

351.  (P)  Mutual  Potential  of  two  Circuits.  —  Two  closed 
circuits  will  have  a  mutual  potential,  depending  on  the  strengths 
of  their  respective  currents,  on  their  distance  apart,  and  on  their 
form  and  position.  If  their  currents  be  respectively  C  and  C', 
and  if  the  distance  between  two  elements  ds  and  ds'  of  the  cir- 
cuits be  called  r,  and  e  the  angle  between  the  elements,  it  can  be 

shown  that  their  mutual  potential  is  =  —  CC'  (    ( ds  ds'. 

This  expression  represents  the  work  that  would  have  to  be  done 
to  bring  up  either  of  the  circuits  from  an  infinite  distance  to  its 
present  position  near  the  other,  and  is  a  negative  quantity  if  they 
attract  one  another.  Now,  suppose  the  strength  of  current  in 
each  cii-cuit  to  be  unity;  their  mutual  potential  will  in  that 

case  be  j   j  —  ^  ds  ds',  a  quantity  which  depends  purely  upon 

the  geometrical  form  and  position  of  the  circuits,  and  for  which 
we  may  substitute  the  single  symbol  M,  which  we  will  call  the 
"  coefficient  of  mutual  potential " :  we  may  now  write  the  mutual 
potential  of  the  two  circuits  when  the  currents  are  C  and  C'  as 
=  -CC'M. 


344  ELECTRICITY   AND   MAGNETISM       PART  n 


But  we  have  seen  in  the  case  of  a  single  circuit  that  we  may 
represent  the  potential  between  a  circuit  and  a  unit-pole  as  the 
product  of  the  strength  of  the  current  —  C  into  the  number  N  of 
the  magnet-pole's  lines  of  force  intercepted  by  the  circuit.  Hence 
the  symbol  M  must  represent  the  number  of  each  other's  lines  of 
force  mutually  intercepted  by  both  circuits,  if  each  carried  unit 
current.  If  we  call  the  two  circuits  A  and  B,  then,  when  each 
carries  unit  current,  A  intercepts  M  lines  of  force  belonging  to 
B,  and  B  intercepts  M  lines  of  force  belonging  to  A. 

Now  suppose  both  currents  to  run  in  the  same  (clock-wise) 
direction;  the  front  or  S-seeking  face  of  one  circuit  will  be 
opposite  to  the  back  or  N-seeking  face  of  the  other  circuit,  and 
they  will  attract  one  another,  and  will  actually  do  work  as  they 
approach  one  another,  or  (as  the  negative  sign  shows)  negative 
work  will  be  done  in  bringing  up  one  to  the  other.  When 
they  have  attracted  one  another  up  as  much  as  possible  the  cir- 
cuits will  coincide  in  direction  and  position  as  nearly  as  can  ever 
be.  Their  potential  energy  will  have  run  down  to  its  lowest 
minimum,  their  mutual  potential  being  a  negative  maximum, 
and  their  coefficient  of  mutual  potential  M,  having  its  greatest 
possible  value.  Two  circuits,  then,  are  urged  so  that  their 
coefficient  of  mutual  potential  M  shall  have  the  greatest  possible 
value.  This  justifies  Maxwell's  Rule  (Art.  204),  because  M 
represents  the  number  of  lines  of  force  mutually  intercepted 
by  both  circuits.  And  since  in  this  position  each  circuit  induces 
as  many  lines  of  magnetic  force  as  possible  through  the  other, 
the  coefficient  of  mutual  potential  M  is  also  called  the  coeffi- 
cient of  mutual  induction  (Art.  454). 

LESSON  XXVII. — The  Electromagnetic  System  of  Units 

352.  Magnetic  Units.  —  All  magnetic  quantities,  strength 
of  poles,  intensity  of  magnetization,  etc.,  are  expressed  in  terms 
of  special  units  derived  from  the  fundamental  units  of  length, 
mass,  and  time,  explained  in  the  Note  on  Fundamental  and 
Derived  Units  (Art.  280).  Most  of  the  following  units  have 
been  directly  explained  in  the  preceding  Lesson,  or  in  Lesson 
XI. ;  the  others  follow  from  them. 

Unit  Magnet-pole.  —  The  unit  magnetic  pole  is  one  of  such 
a  strength,  that  when  placed  at  a  distance  of  1  centi- 
metre (in  air)  from  a  similar  pole  of  equal  strength, 
repels  it  with  a  force  of  1  dyne  (Art.  141) . 
Magnetic  Potential.  —  Magnetic  potential  being  measured 
by  work  done  in  moving  a  unit  magnetic  pole  against  the 


CHAP,  v  ELECTROMAGNETIC    UNITS  345 


magnetic  forces,  the  unit  of  magnetic  potential  will  be 
measured  by  the  unit  of  work  done  on  unit-pole. 

Unit  Difference  of  Magnetic  Potential.— Unit  difference  of 
magnetic  potential  exists  between  two  points  when  it 
requires  the  expenditure  of  one  erg  of  work  to  bring  a 
(N-seeking)  unit  magnetic  pole  from  one  point  to  the 
other  against  the  magnetic  forces.  Magnetomotive-force, 
or  magnetizing  power,  is  measured  in  same  units  as 
difference  of  magnetic  potential. 

Intensity  of  Magnetic  Field  is  measured  by  the  force  it 
exerts  upon  a  unit  magnetic  pole :  hence, 

Unit  Intensity  of  Field  is  that  intensity  of  field  which  acts 
on  a  unit  (N-seeking)  pole  with  a  force  of  1  dyne.  The 
name  of  gauss  has  been  proposed  for  this  unit.  A  field 
having  an  intensity  of  GOOD  lines  per  square  centimetre 
would  be  described  as  G  kilogausses. 

Magnetic  Flux,  or  total  induction  of  magnetic  lines,  is 
equal  to  intensity  of  field  multiplied  by  area.  Its  unit 
will  be  one  magnetic  line. 

Magnetic  Reluctance  (see  Art.  376)  is  the  ratio  of  magneto- 
motive-force to  magnetic  flux.  Unit  reluctance  will  be 
such  that  unit  magnetomotive-force  generates  in  it  a 
flux  of  one  line. 

353.  Electromagnetic  Units.  —  The  preceding  magnetic 
units  give  rise  to  the  following  set  of  electrical  units,  in  which 
the  strength  of  currents,  etc.,  are  expressed  in  magnetic  measure. 
They  are  sometimes  called  "  absolute  C.G.S."  units.  The  relation 
of  this  "electromagnetic"  set  of  units  to  the  "electrostatic" 
set  of  units  of  Art.  283  is  explained  in  Art.  359. 

Unit  Strength  of  Current.— A  current  has  unit  strength  when 
one  centimetre  length  of  its  circuit  bent  into  an  arc  of 
one  centimetre  radius  (so  as  to  be  always  one  centimetre 
away  from  the  magnet-pole)  exerts  a  force  of  one  dyne 
on  a  unit  magnet-pole  placed  at  the  centre  (Art.  207). 

Unit  of  Difference  of  Potential  (or  of  Electromotive-force). 
—  Potential  is  work  done  on  a  unit  of  electricity ;  hence 
unit  difference  of  potential  exists  between  two  points 
when  it  requires  the  expenditure  of  one  erg  of  work  to 
bring  a  unit  of  +  electricity  from  one  point  to  the  other 
against  the  electric  force.  Also,  unit  electromotive-force 
is  generated  by  cutting  one  magnetic  line  per  second. 

Unit  of  Resistance.  —  A  conductor  possesses  unit  resistance 
when  unit  difference  of  potential  between  its  ends  causes 
a  current  of  unit  strength  to  flow  through  it. 


346  ELECTRICITY  AND   MAGNETISM       PART  n 


Unit  of  Quantity  of  Electricity  is  that  quantity  which  is 
conveyed  by  unit  current  in  one  second. 

Unit  of  Capacity.  —  Unit  capacity  requires  unit  quantity  to 
charge  it  to  unit  potential. 

Unit  of  Induction.  —  Unit  induction  is  such  that  unit 
electromotive-force  is  induced  by  the  variation  of  the 
current  at  the  rate  of  one  unit  of  current  per  second. 

354.  Practical  Units  and  Standards.*  —  Several  of  the 
above  "absolute"  units  in  the  C.G.S.  system  would  be  incon- 
veniently large  and  others  inconveniently  small  for  practical 
use.  The  following  are  therefore  chosen  as  practical  units:  — 

Resistance.  —  The  Ohm,  =  10°  absolute  units  of  resistance 
(and  theoretically  the  resistance  represented  by  the 
velocity  of  one  earth-quadrant  per  second,  see  Art.  357), 
but  actually  represented  by  the  resistance  of  a  uniform 
column  of  mercury  106'3  centimetres  long  and  14'4521 
grammes  in  mass,  at  0°  C.  Such  a  column  of  mercury  is 
represented  by  a  "  standard  "  ohm  (see  Appendix  B). 

Current.  —  The  Ampere  (formerly  called  the  "weber"), 
=  10-1  absolute  units ;  practically  represented  by  the 
current  which  deposits  silver  at  the  rate  of  O'OOlllS 
gramme  per  second  (see  Appendix  B). 

Electromotive-force.  —The  Volt,  =  108  absolute  units,  is  that 
E.M.F.  which  applied  to  1  ohm  will  produce  in  it  a 
current  of  1  ampere  ;  being  |£§J  of  the  E.M.F.  of  a 
Clark  standard  cell  at  15'  C.  (See  Appendix  C.) 

Quantity.  —  The  Coulomb,  =  10-1  absolute  units  of  quantity ; 
being  the  quantity  of  electricity  conveyed  by  1  ampere 
in  one  second. 

Capacity.  —  The  Farad,  =  10~9  (or  one  one-thousand- 
millionth)  of  absolute  unit  of  capacity ;  being  the  capa- 
city of  a  condenser  such  as  to  be  changed  to  a  potential 
of  1  volt  by  1  coulomb.  The  microfarad  or  millionth 
part  of  1  farad  =  10~15  absolute  units. 

Work.  —  The  Joule,  =  10"  absolute  units  of  work  (ergs),  is 
represented  by  energy  expended  in  one  second  by  1 
ampere  in  1  ohm. 

Power.  —  The  Watt,  =  10  absolute  units  of  power  (ergs  per 
second),  is  power  of  a  current  of  1  ampere  flowing 

*  The  word  "  unit "  expresses  our  conception  in  the  abstract  of  a  unit 
quantity,  such  as  those  defined  in  the  preceding  Articles.  A  "  standard  " 
is  the  concrete  thing  with  which  we  compare  quantities  to  be  measured, 
such  as  a  centimetre  scale  or  a  standard  cell. 


CHAP,  v  PRACTICAL   UNITS  347 


under  a  pressure  of  1  volt.    It  is  equal  to  1  joule  per 
second,  and  is  approximately  ile  of  one  horse-power. 
Induction.  —  The  Henry,  —  10°  absolute  units  of  induction, 
is  the  induction  in  a  circuit  when  the  electromotive- 
force  induced  in  this  circuit  is  1  volt,  while  the  induc- 
ing current  varies  at  the  rate  of  1  ampere  per  second. 
Seeing,  however,  that  quantities  a  million  times  as  great  as 
some  of  these,  and  a  million  times  as  small  as  some,  have  to  be 
measured  by  electricians,  the  prefixes  mega-  and  micro-  are 
sometimes  used  to  signify  respectively  "  one  million  "  and  "  one- 
millionth  part."    Thus  a  megohm  is  a  resistance  of  one  million 
ohms,  a  microfarad  a  capacity  of  1550555  of  a  farad,  etc.     The 
prefix  kilo-  is  used  for  "one  thousand,"  and  milli-  for  "one- 
thousandth  part " ;    thus  a  kilowatt  is  1000  watts,  and  milli- 
ampere  is  the  thousandth  part  of  1  ampere. 

The  "practical"  system  may  be  regarded  as  a  system  of 
units  derived  not  from  the  fundamental  units  of  centimetre, 
gramme,  and  second,  but  from  a  system  in  which,  while  the 
unit  of  time  remains  the  second,  the  units  of  length  and  mass 
are  respectively  the  earth-quadrant  and  10"11  gramme. 

355.  Use  of  Index  Notation.  —  Seeing  that  electricians  have 
to  deal  with  quantities  requiring  in  some  cases  very  large  num- 
bers, and  in  other  cases  very  small  numbers,  to  express  them,  a 
system  of  index  notation  is  adopted,  in  order  to  obviate  the  use 
of  long  rows  of  ciphers.     In  this  system  the  significant  figures 
only  of  a  quantity  are  put  down,  the  ciphers  at  the  end,  or  (in 
the  case  of  a  long  decimal)  at  the  beginning,  being  indicated  by 
an  index  written  above.     Accordingly,  we  may  write  a  thou- 
sand (=  10  X  10  X  10)  as  103,  and  the  quantity  42,000  may  be 
written  42  X  103.    The  British  National  Debt  of  £770,000,000 
may  be  written  £77  X  107.      Fractional    quantities  will  have 
negative  indices  when  written  as  exponents.    Thus  TOJJ  (—0-01) 
=  1  -*-  10  -T-  10  =  lO-2.      And  so   the  decimal    0-00028  will    be 
written  28  X  10~5  (being  =  28  X  -00001) .    The  convenience  of  this 
method  will  be  seen  by  an  example  or  two  on  electricity.    The 
electrostatic  capacity  of  the  earth  is  630,000,000  times  that  of  a 
sphere  of  one  centimetre  radius,  =  (53  X  10"  (electrostatic)  units. 
The  resistance  of  selenium  is  about  40,000,000,000,  or  4  X  1010 
times  as  great  as  that  of  copper ;  that  of  air  is  about  1026,  or 

100,000,000,000,000,000,000,000,000 

times  as  great.    The  velocity  of  light  is  about  30,000,000,000 
centimetres  per  second,  or  3  X  1010. 

356.  Dimensions  of  Magnetic  and  Electromagnetic   Units. 


348 


ELECTRICITY   AND    MAGNETISM       PART  n 


—  The  fundamental  idea  of  "dimensions"  is  explained  in  Art. 
284.  A  little  consideration  will  enable  the  student  to  deduce  for 
himself  the  following  table :  — 


UNITS. 

DIMENSIONS. 

(Magnetic.) 

m 

<  Strength  of  pole 
'  Quantity  of  magnetism 

Mi  iJ  T-1 

I  =A/force  x  (distance)2          = 

V 

Magnetic  potential 

=  work  4-  strength  of  pole    = 

MiLiT-1 

H 

Intensity  of  field 

=  force  -i-  strength  of  pole     =• 

M2L-ZT"1 

N 

Magnetic  Flux 

=  intensity  x  area 

M*  Li  T-1 

Z 

Reluctance 

=  flux  -f-  mag.  potential        = 

L 

(  Electromagnetic.) 

c 

Current  (strength) 

=  intensity  of  field  x  length  = 

M*L*T    ' 

Q 

Quantity 

=  current  x  time 

Mi  Li 

V 
E 

Potential                    ^ 
Electromotive-force  i 

=  work  -=-  quantity 

Mi  Li  T~2 

R 

Resistance 

=  E.M.F.  -4-  current 

LT-1 

K 

Capacity 

=  quantity  -=-  potential          = 

L-1  T2 

W 

Power 

=  current  x  potential           = 

ML2  T~3 

L 

Self-induction        » 

M 

Mutual  induction  > 

=  E.M.F.-i-  current  per  sec.= 

L 

357.  Resistance  expressed  as  a  Velocity.  — It  will  be  seen, 
on  reference  to  the  above  table  of  "  Dimensions  "  of  electromag- 
netic units,  that  the  dimensions  of  resistance  are  given  as  LT—1, 
which  are  the  same  dimensions  (see  Art.  284)  as  those  of  a  velo- 
city. Every  resistance  is  capable  of  being  expressed  as  a  velocity. 
The  following  considerations  may  assist  the  student  in  forming 
a  physical  conception  of  this.  Suppose  we  have  a  circuit  com- 
posed of  two  horizontal  rails  (Fig.  170),  CS  and  DT,  1  centim. 
apart,  joined  at  CD,  and  completed  by  means  of  a  sliding  piece 
AB.  Let  this  variable  circuit  be  placed  in  a  uniform  magnetic 
field  of  unit  intensity,  the  lines  of  force  being  directed  vertically 
downwards  through  the  circuit.  If,  now,  the  slider  be  moved  along 
towards  ST  with  a  velocity  of  n  centimetres  per  second,the  number 


CHAP,  v         EVALUATION  OF  THE   OHM  349 


of  additional  lines  of  force  embraced  by  the  circuit  will  increase  at 
the  rate  n  per  second ;  or,  in  other  words,  there  will  be  an  induced 
electromotive-force  (Art.  225)  impressed  upon  the  circuit,  which 
will  cause  a  current  to  flow  through  the  slider  from  A  to  B.  Let 
the  rails  have  no  resistance,  then  the  strength  of  the  current  will 
depend  on  the  resistance  of  AB.  Now  let  AB  move  at  such  a 


D  "A.  T 

Fig.  176. 

rate  that  the  current  shall  be  of  unit  strength.  If  its  resistance 
be  one  "  absolute  "  (electromagnetic)  unit  it  need  only  move  at 
the  rate  of  1  centim.  per  second.  If  its  resistance  be  greater  it 
must  move  with  a  proportionately  greater  velocity ;  the  velocity 
at  which  it  must  move  to  keep  up  a  current  of  unit  strength  being 
numerically  equal  to  its  resistance.  The  resistance  known  as 
"  one  ohm  "  is  intended  to  be  109  absolute  electromagnetic  units, 
and  therefore  is  represented  by  a  velocity  of  109  centimetres,  or 
ten  million  metres  (one  earth-quadrant)  per  second. 

358.  Evaluation  of  the  Ohm.  —  The  system  of  "practical" 
units  was  originally  devised  by  a  committee  of  the  British  Asso- 
ciation, who  also  determined  the  value  of  the  "  ohm  "  by  experi- 
ment in  1863,  and  constructed  standard  resistance  coils  of 
german-silver,  called  "B.A.  Units"  or  "ohms." 

There  are  several  ways  of  measuring  the  absolute  value  of  the 
resistance  of  a  wire.  One  method  (Joule's)  is  to  measure  the  heat 
produced  in  it  by  a  known  current  and  calculate  its  resistance  by 
Joule's  law  (Art.  427).  Another  method  (Weber's)  is  to  measure 
in  absolute  units  the  current  that  is  sent  through  the  wire  by  an 
electromotive-force  which  is  also  measured  in  some  absolute  way. 
The  ratio  of  the  latter  to  the  former  gives  the  value  of  the  resist- 
ance. Weber's  method  involved  spinning  a  coil  in  a  magnetic 
field  which  would  generate  alternate  currents.  Kohlrausch  used 
an  induction  coil  to  generate  the  E.M.F.  Lorenz  proposed  a 
method  in  which  a  disk  was  spun .  Foster  a  zero  method  in  which 
the  E.M.F.  in  the  spinning  coil  was  balanced.  Lord  Kelvin  pro- 
posed to  the  British  Association  Committee  a  modification  of 
Weber's  method  as  follows.  It  being  impracticable  to  give  to 
a  horizontal  sliding-piece  so  high  a  velocity  as  was  necessitated, 
the  velocity  which  corresponded  to  the  resistance  of  a  wire  was 
measured  in  the  following  way :  —  a  ring  of  wire  (of  many  turns) , 


350 


ELECTRICITY   AND   MAGNETISM       PART  n 


pivoted  about  a  vertical  axis,  as  in  Fig.  177,  was  made  to  rotate 
very  rapidly  and  uniformly.  Such  a  ring  in  rotating  cuts  the  lines 
of  force  of  the  earth's  magnetism.  The  northern  half  of  the  ring, 
in  moving  from  west  toward  east,  will  have  (see  Rule,  Art.  225)  an 
upward  current  induced  in  it,  while  the  southern  half,  in  crossing 
from  east  toward  west,  will  have  a  downward  current  induced  in 
it.  Hence  the  rotating  ring  will,  as  it  spins,  act  as  its  own  galva- 
nometer if  a  small  magnet  be  hung  at  its  middle ;  the  magnetic 
effect  due  to  the  rotating  coil  being  proportional  directly  to  the 
horizontal  component  of  the  earth's  magnetism,  to  the  velocity  of 

rotation,  and  to  the  number 
of  turns  of  wire  in  the  coil, 
and  inversely  proportional  to 
tne  resistance  of  the  wire  of 
the  coils.  Hence,  all  the  other 
data  being  known,  the  resist- 
ance can  be  calculated  and 
measured  as  a  velocity.  The 


earliest  ohms  or  B.A,  units 
were  constructed  by  compar- 
ison with  this  rotating  coil ; 
but  there  being  some  doubt 
as  to  whether  the  B.A.  unit 
really  represented  109  cen- 
tims.  per  second,  a  redeter- 
mination  of  the  ohm  was 

suggested  in  1880  by  the  British  Association  Committee.  At  the 
first  International  Congress  of  Electricians  in  Paris  1881,  the  pro- 
ject for  a  redetermination  of  the  ohm  was  endorsed,  and  it  was 
also  agreed  that  the  practical  standards  should  no  longer  be  con- 
structed in  German  silver  wire,  but  that  they  should  be  made 
upon  the  plan  originally  suggested  by  Siemens,  by  defining  the 
practical  ohm  as  the  resistance  of  a  column  of  pure  mercury  of  a 
certain  length,  and  of  one  millimetre  of  cross-section.  The  orig- 
inal "Siemens'  unit"  was  a  column  of  mercury  one  metre  in 
length,  and  one  square  millimetre  in  section,  and  was  rather  less 
than  an  ohm  (0'9540  B.A.  unit) .  Acting  on  measurements  made 
by  leading  physicists  of  Europe,  the  Paris  Congress  of  1884  de- 
cided that  the  mercury  column  representing  the  "legal"  ohm 
should  be  106  centimetres  in  length.  This  was,  however,  never 
legalized  in  this  country  or  in  America,  as  it  was  known  to  be 
incorrect.  Lord  Rayleigh's  determination  gave  100*21  centi- 
metres of  mercury,  as  representing  the  true  theoretical  ohm  (  — 
109  absolute  units) ;  and  Rowland's  determinations  at  Baltimore 


RATIO   OF  UNITS 


came  slightly  higher.  The  British  Association  Committee  in  1892 
agreed  to  lengthen  it  to  106'3  centims.,  and  to  define  by  mass 
instead  of  section.  This  was  decided  finally  as  the  international 
ohm  by  the  Congress  of  Chicago  in  1893.  These  international 
units  are  now  legalized  in  England  and  the  United  States.  The 
bulletin  issued  by  the  U.  S.  Superintendent  of  Standard  Weights 
and  Measures,  and  endorsed  by  the  Secretary  of  the  U.  S.  Treas- 
ury, is  given  in  abstract  in  Appendix  B. 

The  old  B. A.  unit  is  only  0'9863  of  the  true  ohm ;  the  Sie- 
mens' unit  is  only  0'9408. 

359.  Ratio  of  the  Electrostatic  to  the  Electromagnetic 
Units.  —  If  the  student  will  compare  the  Table  of  Dimensions  of 
Electrostatic  Units  of  Art.  283  with  that  of  the  Dimensions  of 
Electromagnetic  Units  of  Art.  356,  he  will  observe  that  the  dimen- 
sions assigned  to  similar  units  are  different  in  the  two  systems. 
Thus,  the  dimensions  of  "Quantity"  in  electrostatic  measure 
are  M*  ll  T"1,  and  in  electromagnetic  measure  they  are  M*  L*- 
Dividing  the  lormer  by  the  latter  we  get  LT~  >  a  quantity  which 
we  at  once  see  is  of  the  nature  of  a  velocity.  This  velocity  occurs 
in  every  case  in  the  ratio  of  the  electrostatic  to  the  electromag- 
netic measure  of  every  unit.  It  is  a  definite  concrete  velocity, 
and  represents  that  velocity  at  which  two  electrified  particles 
must  travel  along  side  by  side  in  order  that  their  mutual  electro- 
magnetic attraction  (considered  as  equivalent  in  so  moving  (Art. 
397)  to  two  parallel  currents)  shall  just  equal  their  mutual  elec- 
trostatic repulsion  (see  Art.  260).  This  velocity,  "  v,"  which  is 
of  enormous  importance  in  the  electromagnetic  theory  of  light 
(Art.  518),  has  been  measured  in  several  ways. 


UNIT. 

ELECTROSTATIC. 

ELECTROMAGNETIC. 

EATIO. 

Quantity    . 

M*L*     T"1 

M*L* 

LT"1   =v 

Potential    . 

M*I>    T'1 

M*  L*  T-2 

IT1  T  =  l/v 

Capacity    . 

L 

L-1T2 

L2  T~2=  v2 

Resistance  . 

L-i  T 

L     T"1 

L~2T2=W 

(a)  Weber  and  Kohlrausch  measured  the  electrostatic  unit  of 
quantity  and  compared  it  with  the  electromagnetic  unit  of  quan- 
tity, and  found  the  ratio  v  to  be=3-1074x  1010  centims.  per  second. 


352  ELECTRICITY   AND   MAGNETISM       PART  11 

(b)  Lord  Kelvin  compared  the  two  units  of  potential  and 
found 

v        =  2-825     X  101°, 
and  later,        =  2'93      X  1010. 

(c)  Professor  Clerk  Maxwell  balanced  a  force  of  electrostatic 
attraction  against  one  of  electromagnetic  repulsion,  and  found 

v        =  2-88        X   1010. 

(d)  Professors  Ayrtou  and  Perry  measured  the  capacity  of  a 
condenser  electromagnetically  by  discharging  it  into  a  ballistic 
galvanometer,  and  electrostatically  by  calculations  from  its  size, 
and  found 

v        =  2-980      X  1010. 
The  velocity  of  light  according  to  latest  values  is  — 

=  2-9992     X   101°; 

so  we  take  v  as  3  x  1010,  or  thirty  thousand  million  centimetres 
per  second. 

360.  Rationalization  of  Dimensions  of  Units.  —  It  seems  ab- 
surd that  there  should  be  two  different  units  of  electricity ;  still 
more  absurd  that  one  unit  should  be  thirty  thousand  million  centi- 
metres per  second  greater  than  the  other.     It  also  seems  absurd 
that  the  dimensions  of  a  unit  of  electricity  should  have  fractional 
powers,  since  such  quantities  as  M*  and  iJ  are  meaningless. 
These  irrational  things  arise  from  the  neglect  to  take  account  of 
the  properties  of  the  medium  in  applying  the  law  of  inverse 
squares  to  form  definitions  of  the  unit  of  electricity  in  the 
electrostatic  system,  and  of  the  unit-pole  in  the  magnetic  system. 
If  we  were  to  insert  the  dielectric  constant  k  in  the  former,  and  the 
permeability  t*-  in  the  latter,  we  might,  if  we  knew  the  dimensions 
of  these  quantities,  be  able  to  rationalize  the  dimensional  formu- 
lae.   But  we  do  not  know  their  dimensions.    Riicker  has,  however, 
shown  that  they  can  be  rationalized,  and  the  two  sets  of  units 
brought  into  agreement,*  by  assuming  that  the  product  kp.  has 
the  dimensions  of  the  reciprocal  of  the  square  of  a  velocity :  or 
v  =  l/7l>.    If  k  were  the  reciprocal  of  the  rigidity  of  the  ether, 
and  M  its  density,  v  would  represent  the  velocity  of  propagation  of 
waves  in  it.   Compare  Art.  518  on  electromagnetic  theory  of  light. 

361.  Earth's  Magnetic  Force  in  Absolute  Units.  — In  mak- 
ing absolute  determinations  of  current  by  the  tangent  galva- 
nometer, or  of  electromotive-force  by  the  spinning  coil,  it  is  need- 
ful to  know  the  absolute  value  of  the  earth's  magnetic  field,  or 
of  its  horizontal  component.     The  intensity  of  the  earth's  mag- 
netic force  at  any  place  is  the  force  with  which  a  magnet-pole  of 

*  See  Everett's  Units  and  Physical  Constants,  4th  edition  (1893),  p.  208. 


CHAP,  v         MAGNETIC   MEASUREMENTS  353 


unit  strength  is  attracted.  As  explained  in  Art.  153,  it  is  usual 
to  measure  the  horizontal  component  H  of  this  force,  and  from 
this  and  the  cosine  of  the  angle  of  dip  to  calculate  the  total 
force,  as  the  direct  determination  of  the  latter  is  surrounded  with 
difficulties.  To  determine  H  in  absolute  (or  C.G.S.)  units,  it  is 
necessary  to  make  two  observations  with  a  magnet  of  magnetic 
moment  M  (Art.  135) .  In  one  of  these  observations  the  product 
MH  is  determined  by  a  method  of  oscillations  (Art.  133) ;  in  the 

second  the  quotient  —  is  determined  by  a  particular  method  of 

H 

deflexion  (Art.  138).  The  square  root  of  the  quantity  obtained 
by  dividing  the  former  by  the  latter  will,  of  course,  give  H. 

(i.)  Determination  of  MH. — The    time  T  of  a  complete 
oscillation  to  and  fro  of  a  magnetic  bar  is 

T  =  2* 

where  K  is  the  " moment  of  inertia"  of  the  magnet.  This  for- 
mula is,  however,  only  true  for  very  small  arcs  of  vibration. 
By  simple  algebra  it  follows  that 


Of  these  quantities  T  is  ascertained  by  a  direct  observation 
of  the  time  of  oscillation  of  the  magnet  hung  by  a  torsionless 
fibre;  and  K  can  be  either  determined  experimentally  or  by 
one  of  the  following  formulae :  — 

For  a  round  bar  ~K  —  w[—  +  —  ), 

\12      */ 

For  a  rectangular  bar    K  =  w  I—    -  J ; 

where  to  is  the  mass  of  the  bar  in  grammes,  I  its  length,  a  its 
radius  (if  round),  6  its  breadth,  measured  horizontally  (if  rec- 
tangular) . 

(ii.)  Determination  of— .—  The  magnet  is  next  caused  to 

H 

deflect  a  small  magnetic  needle  in  the  following  manner,"  broad- 
side on."  The  magnet  is  laid  horizontally  at  right  angles  to  the 
magnetic  meridian,  and  so  that  its  middle  point  is  (magnetically) 
due  south  or  due  north  of  the  small  needle,  and  at  a  distance  r 
from  its  centre.  Lying  thus  broadside  to  the  small  needle  its 
N  pole  will  repel,  and  its  S  pole  attract,  the  N  pole  of  the  needle, 
and  will  exercise  contrary  actions  on  the  S  pole  of  the  needle. 
The  total  action  of  the  magnet  upon  the  needle  will  be  to  deflect 
the  latter  through  an  angle  5,  whose  tangent  is  directly  propor- 
2A 


354  ELECTRICITY    AND   MAGNETISM       PART  n 


TVT 

tional  to  — ,  and  inversely  proportional  to  the  cube  of  the  dis- 

M 

tance  r ;  or  —  =  r3  tan  S. 

H 

Dividing  the  former  equation  by  this,  and  taking  the  square 
root,  we  get 


LESSON  XXVIII.  —  Properties  of  Iron  and  Steel 

362.  Magnetization  of  Iron.  —  When  a  piece  of  mag- 
netizable metal  is  placed  in  a  magnetic  field,  some  of  the 
lines  of  magnetic  force  run  through  it  and  magnetize  it. 
The  intensity  of  its  magnetization  will  depend  upon  the 
intensity  of  the  field  into  which  it  is  put  and  upon  the 
metal  itself.   There  are  two  ways  of  looking  at  the  matter, 
each  of  which  has  its  advantages.     We  may  think  about 
the  internal  condition  of  the  piece  of  metal,  and  of  the 
number  of   magnetic  lines  that  are  running  through  it 
and  emerging  from  it  into  the  surrounding  space.     This 
is  the  modern  way.     Or  we  may  think  of  the  magnetism 
of  the  iron  or  other  metal  as  something  resident  on  the 
polar  surfaces,  and  expressed  therefore  in  units  of  mag- 
netism.    This  is  the  old  way.     The  fact  that  soft  iron 
placed  in  the  magnetic  field  becomes  highly  magnetic  may 
then  be  expressed  in  the  following  two  ways :  (1)  when 
iron  is  placed  in  the  magnetic  field,  the  magnetic  lines  run 
in  greater  quantities  through  the  space  now  occupied  by 
iron,  for  iron  is  very  permeable  to  the  lines  of  magnetic 
induction,  being  a  good  conductor  of  the  magnetic  lines ; 
(2)  iron   when    placed   in  the   magnetic   field   develops 
strong  poles  on  its  end-surfaces,  being  highly  susceptible 
to  magnetization.     Each  of  these  ideas  may  be  rendered 
exact  by  the  introduction  of  appropriate  coefficients. 

363.  Permeability.  —  The    precise   notion   now   at- 
tached to  this  word   is  that  of  a  numerical   coefficient. 
Suppose  a  magnetic  force  —  due,  let  us  say,  to  the  circula- 
tion of  an  electric  current  in  a  surrounding  coil  —  were  to 


CHAP,  v  PERMEABILITY  355 

act  on  a  space  occupied  by  air,  there  would  result  a  certain 
number  of  magnetic  lines  in  that  space.  In  fact,  the 
intensity  of  the  magnetic  force,  symbolized  by  the  letter 
H,  is  often  expressed  by  saying  that  it  would  produce  H 
magnetic  lines  per  square  centimetre  in  air.  Now,  owing 
to  the  superior  magnetic  power  of  iron,  if  the  space 
subjected  to  this  magnetic  force  were  filled  with  iron 
instead  of  air,  there  would  be  produced  a  larger  number 
of  magnetic  lines  per  square  centimetre.  This  larger 
number  of  magnetic  lines  in  the  iron  expresses  the 
degree  of  magnetization  *  in  the  iron  ;  it  is  symbolized 
by  the  letter  B.  The  ratio  of  B  to  H  expresses  the 
permeability  of  the  material.  The  usual  symbol  for  per- 
meability is  the  Greek  letter  /A.  So  we  may  say  that  B 
is  equal  to  //,  times  H,  or 


For  example,  a  certain  specimen  of  iron,  when  sub- 
jected to  a  magnetic  force  capable  of  creating,  in  air,  50 
magnetic  lines  to  the  square  centimetre,  was  found  to  be 
permeated  by  no  fewer  than  16,062  magnetic  lines  per 
square  centimetre.  Dividing  the  latter  figure  by  the 
former  gives  as  the  value  of  the  permeability  at  this 
stage  of  the  magnetization  321,  or  the  permeability  of 
the  iron  is  321  times  that  of  air. 

The  permeability  is  always  positive  :  for  empty  space 
it  is  1,  for  air  it  is  practically  1  ;  for  magnetic  materials 
it  is  greater  than  1,  for  diamagnetic  materials  it  is  slightly 
less  than  1.  In  air,  etc.,  B  =  H. 

Where  the  magnetic  lines  emerge  into  the  air  at  a 
polar  surface  they  are  of  course  continuous  with  the 
internal  lines  :  the  value  of  B  just  inside  the  polar  sur- 
face is  the  same  as  that  of  B  in  the  air  just  outside  it. 

The  permeability  of  such  non-magnetic  materials  as 

*  The  actual  number  of  magnetic  lines  that  run  through  unit  area  of 
cross-section  in  the  iron  or  other  material  —  denoted  by  the  symbol  B  —  is 
called  by  several  names  —  "  the  permeation,"  "  the  internal  magnetization," 
or  "the  induction."  The  last  name,  unfortunately  used  by  Maxwell  and 
Hopkinson,  is  to  be  avoided.  A  better  name  is  "  flux  density." 


356  ELECTRICITY  AND   MAGNETISM      PART  11 

silk,  cotton,  and  other  insulators,  also  of  brass,  copper, 
and  all  the  non-magnetic  metals,  is  taken  at  1,  being 
practically  the  same  as  that  of  the  air. 

This  mode  of  expressing  the  facts  is,  however,  com- 
plicated by  the  fact  of  the  tendency  in  all  kinds  of  iron 
to  magnetic  saturation.  In  all  kinds  of  iron  the  rnag- 
netizability  of  the  material  becomes  diminished  as  the 
actual  magnetization  is  pushed  further.  In  other  words, 
when  a  piece  of  iron  has  been  magnetized  up  to  a  certain 
degree,  it  becomes,  from  that  degree  onward,  less  perme- 
able to  further  magnetization,  and  though  actual  satura- 
tion is  never  reached,  there  is  a  practical  limit  beyond 
which  it  cannot  well  be  pushed.  Joule  discovered  this 
tendency  to  a  limit.  The  practical  limit  of  B  in  good 
wrought  iron  is  about  20,000  lines  per  square  centimetre, 
or  in  cast  iron  about  12,000.  Using  extraordinary  mag- 
netizing forces,  Ewing  has  found  it  possible  to  increase 
B  to  45,000,  and  Du  Bois  has  reached  60,000  lines  per 
square  centimetre.  Manganese  steel  is  curiously  non- 
magnetic: Hopkinson  found  310  as  the  maximum  B. 

364.  Curves  of  Magnetization.  —  A  convenient  mode 
of  studying  the  magnetic  facts  respecting  any  particular 

brand  of  iron  is  to  plot  on  a 
diagram  the  curve  of  mag- 
netization —  i.e.  the  curve  in 
which  the  values,  plotted 
horizontally,  represent  the 
magnetic  force  H,  and  the 
values  plotted  vertically  those 
that  correspond  to  the  respec- 
tive magnetization  B.  In  Fig. 
178,  which  is  modified  from 
the  researches  of  Ewing,  are  given  five  curves  relating 
to  soft  iron,  hardened  iron,  annealed  steel,  hard-drawn 
steel,  and  glass-hard  steel.  It  will  be  noticed  that  all 
these  curves  have  the  same  general  form,  and  that  there 
are  three  stages.  (1)  For  small  values  of  H  the  values  of 


CHAP,  v       CURVES   OF   MAGNETIZATION 


357 


B  are  small,  and  as  H  is  increased  B  increases  gradually. 
(2)  The  curve  rises  very  suddenly,  at  least  with  all  the 
softer  sorts  of  iron.  (3)  The  curve  then  bends  over  and 
becomes  nearly  horizontal,  B  increasing  very  slowly. 
When  the  magnetization  is  in  the  stage  below  the  bend 
of  the  curve,  the  iron  is  said  to  be  far  from  the  state  of 
saturation.  But  when  the  magnetization  has  been  pushed 
beyond  the  bend  of  the  curve  into  the  third  stage,  the 
iron  is  said  to  be  approaching  saturation,  because  at  this 
stage  of  magnetization  it  requires  a  large  increase  in  the 
magnetizing  force  to  produce  even  a  very  small  increase 
in  the  magnetization.  It  will  be  noted  that  for  soft 
wrought  iron  the  stage  of  approaching  saturation  sets  in 
when  B  has  attained  the  value  of  about  16,000,  or  when 
H  has  been  raised  to  about  50.  The  student  is  strongly 
advised  to  plot  for  himself  similar  curves  from  the  sub- 
joined table,  which  relates  to  the  permeabilities  of  some 
samples  of  iron  examined  by  Hopkinson. 


ANNEALED  WROUGHT  IRON. 

GREY  CAST  IRON. 

B 

/"• 

H 

B 

M 

H 

5,000 

3000 

1-66 

4,000 

800 

5 

9,000 

2250 

4 

5,000 

500 

10 

10,000 

2000 

5 

6,000 

279 

21-5 

11,000 

1692 

6-5 

7,000 

133 

42 

12,000 

1412 

8-5 

8,000 

100 

80 

13,000 

1083 

12 

9,000 

71 

127 

14,000 

823 

17 

10,000 

53 

188 

15,000 

526 

28-5 

11,000 

37 

292 

16,000 

320 

50 

17,000 

161 

105 

18,000 

90 

200 

19,000 

54 

350 

20,000 

30 

666 

It  will  be  noted  that  at  early  stages  of  the  magnetiza- 


358  ELECTRICITY   AND   MAGNETISM      PART  n 

tion,  in  moderately  weak  fields  where  H  is  less  than 
about  5,  the  permeability  has  enormous  values.  But 
for  values  of  H  less  than  about  0-5  the  permeability  is 
quite  small,  usually  about  300. 

The  three  stages  observed  in  the  magnetization  are 
explained  in  Ewing's  molecular  theory  (Art.  127). 

If  iron  is  compressed  its  permeability  decreases  ;  if 
subjected  to  tensile  stress  it  is  increased,  provided  the 
field  is  not  too  intense.  Villari  found  that  beyond  a  cer- 
tain intensity  tension  diminishes  the  permeability. 

365.  Susceptibility.  —  Suppose  a  magnet  to  have 
m  units  of  magnetism  on  each  pole  ;  then  if  the  length 
between  its  poles  is  Z,  the  product  ml  is  called  its  magnetic 
moment,  and  the  magnetic  moment  divided  by  its  volume 
is  called  its  intensity  of  magnetization  ;  this  term  being 
intended,  though  based  on  surface-unit  of  pole  strength, 
to  convey  an  idea  as  to  the  internal  magnetic  state. 
Seeing  that  volume  is  the  product  of  sectional  area  into 
length,  it  follows  that  if  any  piece  of  iron  or  steel  of 
uniform  section  had  its  surface  magnetism  situated  on  its 
ends  only,  its  intensity  of  magnetization  would  be  equal 
to  the  strength  of  pole  divided  by  the  area  of  end-surface. 
Writing  I  for  the  intensity  of  magnetization  we  should 
have 

I  _  mag.  moment  _  m  X  I  _m 
volume  s  X  I       s 

Now,  supposing  this  intensity  of  magnetization  were 
due  to  the  iron  having  been  put  into  a  magnetic  field  of 
intensity  H,  the  ratio  between  the  resulting  intensity  of 
magnetization  I  and  the  magnetizing  force  H  producing 
it  is  expressible  by  a  numerical  coefficient  of  magnetiza- 
tion, or  susceptibility,  k.  We  may  write 


or  k  =  I/H. 

This   may  be  looked  at  as  saying  that  for  every 


CHAP.    V 


LIMIT   OF   MAGNETIZATION 


359 


magnetic  line  in  the  field  there  will  be  k  units  of 
magnetism  on  the  end-surface.  In  magnetic  substances 
such  as  iron,  steel,  nickel,  etc.,  the  susceptibility  k  has 
positive  values ;  but  there  are  many  substances  such  as 
bismuth,  copper,  mercury,  etc.,  which  possess  feeble 
negative  coefficients.  These  latter  are  termed  "  diamag- 
netic  "  bodies  (Art.  369)  and  are  apparently  repelled  by 
the  poles  of  magnets.  It  was  shown  at  end  of  Art.  338 
that  there  are  4?r  magnetic  lines  proceeding  from  each 
unit  of  pole  magnetism.  Hence  if,  as  shown  above,  each 
line  of  force  of  the  magnetizing  field  produces  k  units  of 
magnetism  there  will  be  4^  lines  added  by  the  iron  to 
each  1  line  in  the  field,  or  the  permeability  of  the  iron 
/x  is  equal  to  1  -f  kirk.  It  follows  that  B  =  H  +  47r£H. 
This  shows  that  B  may  go  011  increasing  as  long  as  H 
is  increased,  having  no  true  limit.  But  since  k  decreases 
as  saturation  sets  in,  the  surface  magnetization  I  (or  B  —  H 
to  which  it  is  proportional)  may  have  a  true  limit.  This 
maximum  of  B  —  H  appears  to  be  about  21,360  in 
wrought  iron,  15,580  in  cast  iron,  and  5660  in  nickel. 

In  the  following  table  are  given  some  figures  from 
the  researches  of  Bidwell  on  wrought  iron. 


H 

t 

I 

M 

B 

3-9 

151-0 

587 

1899-1 

7390 

10-3 

89-1 

918 

1121-4 

11550 

40- 

30-7 

1226 

386-4 

15460 

115- 

11-9 

1370 

150-7 

17330 

208- 

7-0 

1452 

88-8 

18470 

427- 

3-5 

1504 

45-3 

19330 

585- 

2-6 

1530 

33-9 

19820 

Everett  has  calculated  (from  Gauss's  observations) 
that  the  intensity  of  magnetization  of  the  earth  is  only 
0-0790,  or  only  J^-Q-Q  of  what  it  would  be  if  the  globe 


360  ELECTRICITY  AND   MAGNETISM      PART  n 

were  wholly  iron.  In  weak  magnetic  fields  the  suscep- 
tibility of  nickel  exceeds  by  about  five  times  that  of  iron ; 
but  in  strong  fields  iron  is  more  susceptible. 

366.  Measurement    of    Permeability.  —  There    are 
several  ways  of  measuring  the  permeability  of  iron  :  they 
all  involve  a  measurement  of  B. 

(a)  Magnetometer  Methods.  —  The  pole  strength  of  long 
bars,  when  magnetized  by  a  coil  around   them,  can  be 
measured  by  a  magnetometer  (Art.  138),  and  from  this 
N  is  found  by  multiplying  by  4?r. 

(b)  Induction  Methods.  —  Rings  of  iron  which,  having 
no  poles,  cannot  be  measured  by  the  magnetometer  are 
measured  inductively.     Upon  the  ring  is  wound  a  mag- 
netizing coil,  and  also  an  exploring  coil  (Art.  232)  which 
is  connected  to  a  ballistic  galvanometer.      On  turning  on 
or  off  the  magnetizing  current,  or  reversing  it,  induced 
currents   are  generated,  giving   a  throw   in  the   galva- 
nometer proportional  to  the  number  of   magnetic  lines 
which  have  been  made  or  destroyed.      Iron  rods  can  be 
examined  by  the  same  means. 

(c)  Traction  Methods.  —  The  pull  needed  to  separate 
the  two  halves  of  a  divided  rod,  or  divided  ring,  is  (Art. 
384)  proportional  to  the  square  of  B.     Bidwell  and  others 
have  used  this  for  measuring  permeability. 

(t/)  Optical  Methods.  —  Da  Bois  has  used  a  method 
based  on  Kerr's  discovery  (Art.  527)  of  magneto-optic 
rotation. 

367.  Residual    Effects.  —  The    retention    of    mag- 
netism by  steel,  lodestone,  hard  iron,  and  even  by  soft 
iron  if  of  elongated  shape,  has  been  already  described 
(Art.  98).      Some  other  residual  effects   must  now  be 
noted.     It  is  found  that  if  a  new  piece  of  iron  or  steel  is 
subjected  to  an  increasing  magnetizing  force,  and  then  the 
magnetizing  force  is  decreased  to  zero,  some  magnetism 
remains.      If   the  results  are  plotted  out  in  a  curve  it 
exhibits  the  following  peculiarities.     On  first  gradually 
increasing  H  from  o,  B  rises  as  we  have  seen  in  Art.  364. 


CHAP,  v        CYCLES   OF   MAGNETIZATION 


361 


If  when  the  curve  has  risen  to  a  (Fig.  179)  H  is  now 
decreased,  the  descending  curve  does  not  follow  the 
ascending  curve,  owing  to  the  retention  of  the  magne- 
tism. When  H  has  been  reduced  to  zero  the  point  b  is 
reached.  This  the  residual  value 
of  B  is  called  the  remanence,  and 
depends  on  the  material,  and  on 
the  degree  to  which  B  was  pre- 
viously pushed.  If  now  a  re- 
versed magnetizing  force  —  H  is 
now  applied  it  is  found  that  it 
must  be  increased  to  a  definite 
degree  in  order  to  demagnetize 
the  iron  and  bring  the  curve  down 
to  c.  The  amount  of  reversed 
magnetic  force  so  needed  is  a 
measure  of  the  reteiitivity  of  the 
material,  and  is  known  as  the 
coercive  force.  In  hard  steel  it  may  amount  to  100 ;  in 
soft  steel  to  20  ;  in  soft  iron  to  2  or  less.  If  the  reversed 
magnetizing  force  is  further  increased,  the  curve  descends 
from  c  to  d,  the  iron  becoming  magnetized  with  reversed 
polarity,  and  going  toward  saturation.  On  then  dimin- 
ishing the  reversed  force  to  zero,  the  curve  turns  to  e, 
showing  a  negative  remanence.  On  again  increasing  H 
as  at  first  the  curve  ascends  to  f,  and  as  the  former  value 
of  H  is  reached  conies  up  to  a  again. 

368.  Cycles  of  Magnetization.  Hysteresis.  —  When 
H  is  thus  carried  through  a  cycle  of  increase  and 
decrease,  B  also  goes  through  a  cycle ;  and  as  we  have 
seen  there  is  a  lagging  in  the  magnetization,  evidenced  in 
Fig.  179  by  the  formation  of  a  closed  loop  in  the  curve. 
Warburg  and  Ewing,  who  have  fully  investigated  the 
phenomenon,  have  remarked  that  the  area  enclosed 
indicates  the  waste  of  energy  in  the  cycle  of  operations. 
In  hard  steel  the  areas  of  these  loops  are  much  wider 
than  in  the  case  of  soft  iron.  Ewing  has  given  the  name 


ELECTRICITY   AND   MAGNETISM      PART  n 


of  Hysteresis  to  the  subject  of  the  lag  of  magnetic  effects 
behind  their  causes.  From  his  researches  *  also  is  taken 
the  case  of  Fig.  180,  a  specimen  of  soft  iron,  the  curve 
for  which  shows  various  loops.  Ewing  has  devised  a 
curve-tracer  for  recording  the  curves  automatically.  The 

waste  of  energy  per  cubic 
centimetre  in  a  cycle  of 
strong  magnetization  may 
vary  from  9000  ergs  in 
annealed  iron  to  200,000 
in  glass-hard  steel.  If  (as 
in  the  iron  cores  of  alter- 
nate current  transformers) 
the  cycle  is  repeated  100 
times  a  second  the  waste 
of  power  by  hysteresis  may 
heat  the  iron;  and  it  in- 
creases greatly  with  the 
frequency  and  with  the 
degree  to  which  the  mag- 
netization is  pushed.  If  B 
does  not  exceed  5000,  the 
power  wasted  at  100  cycles 
per  second  in  every  cubic 
foot  of  iron  may  be  as  low 
as  575  watts,  but  if  B  is  increased  to  10,000  the  waste 
becomes  1560  watts. 

Since  a  smaller  reversed  force  suffices  tb  destroy  mag- 
netization than  was  required  to  produce  it,  all  that  is 
necessary  in  order  to  completely  demagnetize  iron  is  to 
subject  it  to  a  series  of  cycles  of  diminishing  intensity. 

Mechanical  agitation  tends  to  help  the  magnetizing 
forces  to  act,  and  lessens  all  residual  and  hysteresial 
effects. 

Ewing  has  also  shown  that  under  constant  magnetizing 

*  The  student  should  not  fail  to  consult  Ewing's  book,  Magnetic  In- 
duction in  Iron. 


CHAP.    V 


DIAMAGNETISM 


303 


force  the  magnetism  will  go  on  slowly  and  slightly  in- 
creasing for  a  long  time  :  this  is  called  magnetic  creep- 
ing, or  viscous  hysteresis. 


LESSON  XXIX.  —  Diamagnetism 

369.  Diamagnetic  Experiments.  —  In  1778  Brugmans 
of  Leyden  observed  that  when  a  lump  of  bismuth  was 
held  near  either  pole  of  a  magnet  needle  it  repelled 
it.  In  1827  Le  Baillif  and  Becquerel  observed  that  the 
metal  antimony  also  could  repel  and  be  repelled  by  the 
pole  of  a  magnet.  In  1845  Faraday,  using  powerful 
electromagnets,  examined  the  magnetic  properties  of  a 
large  number  of  substances,  and  found  that  whilst  a 
great  many  are,  like  iron,  attracted  to  a  magnet,  others 
are  feebly  repelled.  To  distinguish  between  these  two 
classes  of  bodies,  he  termed  those  which  are  attracted 
paramagnetic,*  and  those  which  are  repelled  diamagnetic. 
The  property  of  being  thus  apparently  repelled  from  a 
magnet  he  termed  diamagnetism. 

Faraday's  method  of  experiment  consisted  in  suspend- 
ing a  small  bar  of  the  substance  in 
a  powerful  magnetic  field  between 
the  two  poles  of  an  electromagnet, 
and  observing  whether  the  small 
bar  was  attracted  into  an  axial 
position,  as  in  Fig.  181,  with  its 
length  along  the  line  joining  the 
two  poles,  or  whether  it  was  re- 
pelled into  an  equatorial  position, 
at  right  angles  to  the  line  joining 
the  poles,  across  the  lines  of  force 
of  the  field,  as  is  shown  by  the  position  of  the  small  bar 
in  Fig.  182,  suspended  between  the  poles  of  an  electro- 
magnet constructed  on  RuhmkorfFs  pattern. 

*  Or  simply  "magnetic."  Some  authorities  use  the  term  "ferro- 
magnetic." 


Fig.  181. 


364 


ELECTRICITY  AND   MAGNETISM     PART  n 


Fig.  182. 

37O.    Results.  —  The  following  are  the  principal  sub- 
stances examined  by  the  method :  — 


PARAMAGNETIC. 

DlAMAGNETIC. 

Iron 

Bismuth 

Nickel 

Phosphorus 

Cobalt 

Antimony 

Manganese 

Thallium 

Chromium 

Zinc 

Cerium 

Mercury 

Titanium 

Lead 

Platinum  * 

Silver 

Many  ores  and  salts 

Copper 

containing  the 

Gold 

above  metals 

Water 

Oxygen  gas 

Alcohol 

Oxygen  liquid 

Tellurium 

Ozone 

Sulphur 

*  Chemically  pure  Platinum  is  diamagnetic,  according  to  Wiedeinann. 


DIAMAGNETISM  365 


Liquids  were  placed  in  glass  vessels  and  suspended 
between  the  poles  of  the  electromagnet.  Almost  all 
liquids  are  diamagnetic,  except  solutions  of  salts  of  the 
magnetic  metals,  some  of  which  are  feebly  magnetic ;  but 
blood  is  diamagnetic  though  it  contains  iron.  To  examine 
gases  bubbles  are  blown  with  them,  and  watched  as  to 
whether  they  were  drawn  into  or  pushed  out  of  the  field. 
Oxygen  gas  was  found  to  be  magnetic ;  ozone  has  been 
found  to  be  still  more  strongly  so.  Dewar  has  found 
liquid  oxygen  sufficiently  magnetic  to  rush  in  drops  to  the 
poles  of  a  powerful  magnet. 

The  diamagnetic  properties  of  substances  may  be 
numerically  expressed  in  terms  of  their  permeability  or 
their  susceptibility  (Arts.  363  and  365).  For  diamagnetic 
bodies  the  permeability  is  less  than  unity.  For  bismuth 
the  value  of  /x,  is  0-999969.  The  repulsion  of  bismuth  is 
immensely  feebler  than  the  attraction  of  iron.  Pliicker 
estimated  the  relative  magnetic  powers  of  equal  weights 
of  substances  as  follows :  — 

Iron  +  1,000,000 

Lodestone  Ore  +  402,270 

Ferric  Sulphate  +  1,110 

Ferrose  Sulphate  +  780 

Water  7'8 

Bismuth  23'6 

371.  Apparent  Diamagnetism  due  to  surrounding 
Medium.  —  It  is  found  that  feebly  magnetic  bodies  be- 
have as  if  they  were  diamagnetic  when  suspended  in  a 
more  highly  magnetic  fluid.  A  small  glass  tube  filled 
with  a  weak  solution  of  ferric  chloride,  when  suspended 
in  air  between  the  poles  of  an  electromagnet,  points 
axially,  or  is  paramagnetic ;  but  if  it  be  surrounded  by 
a  stronger  (and  therefore  more  magnetic)  solution  of 
the  same  substance,  it  points  equatorially,  and  is  appar- 
ently repelled  like  diamagnetic  bodies.  All  that  the 
equatorial  pointing  of  a  body  proves  then  is,  that  it  is  less 
magnetic  than  the  medium  that  fills  the  surrounding  space. 


366  ELECTRICITY  AND   MAGNETISM      PART  n 

A  balloon,  though  it  possesses  mass  and  weight,  rises 
through  the  air  in.  obedience  to  the  law  of  gravity,  because 
the  medium  surrounding  it  is  more  attracted  than  it  is. 
But  it  is  found  that  diamagnetic  repulsion  takes  place  even 
in  a  vacuum :  hence  it  would  appear  that  the  ether  of 
space  itself  is  more  magnetic  than  the  substances  classed 
as  diamagnetic. 

372.  Diamagnetic  Polarity.  —  At  one  time  Faraday 
thought  that  diamagnetic  repulsion  could  be  explained 
on  the  supposition  that  there  existed  a  "  diamagnetic 
polarity "  the  reverse  of  the  ordinary  magnetic  polarity. 
According  to  this  view,  which,  however,  Faraday  himself 
quite  abandoned,  a  magnet,  when  its  N  pole  is  presented 
to  the  end  of  a  bar  of  bismuth,  induces  in  that  end  a 
N  pole  (the  reverse  of  what  it  would  induce  in  a  bar  of 
iron  or  other  magnetic  metal),  and  therefore  repels  it. 
Weber  adopted  this  view,  and  Tyndall  warmly  advocated 
it,  especially  after  discovering  that  the  repelling  diamag- 
netic force  varies  as  the  square  of  the  magnetic  power 
employed.  It  has  even  been  suggested  that  when  a 
diamagnetic  bar  lies  equatorially  across  a  field  of  force,  its 
east  and  west  poles  possess  different  properties.  The  ex- 
periments named  above  suggest,  however,  an  explanation 
less  difficult  to  reconcile  with  the  facts.  It  has  been 
pointed  out  (Art.  363)  that  the  degree  to  which  mag- 
netization goes  on  in  a  medium  depends  upon  the  magnetic 
permeability  of  that  medium.  Now,  permeability  ex- 
presses the  number  of  magnetic  lines  induced  in  the 
medium  for  every  line  of  magnetizing  force  applied.  A 
certain  magnetizing  force  applied  to  a  space  containing  air 
or  vacuum  would  induce  a  certain  number  of  magnetic 
lines  through  it.  If  the  space  considered  were  occupied 
by  a  paramagnetic  substance  it  would  concentrate  the 
magnetic  lines  into  itself,  as  the  sphere  does  in  Fig.  183. 
But  if  the  sphere  were  of  a  permeability  less  than  1,  the 
magnetic  lines  would  tend  rather  to  pass  through  the  air, 
as  in  Fig.  184.  If  the  space  considered  were  occupied  by 


CHAP.    V 


DIAMAGNETIC   ACTION 


367 


bismuth,  the  same  magnetizing  force  would  induce  in  the 
bismuth  fewer  magnetic  lines  than  in  a  vacuum.     But 
those  lines  which  were  induced     _^______ 

would  still  run  in  the  same 
general  direction  as  in  the 
vacuum;  not  in  the  opposite 
direction,  as  Weber  and  Tyndall 
maintained.  The  result  of 
there  being  a  less  induction 
through  diamagnetic  sub-  Fig.  183. 

tances   can  be  shown  to  be  that  such   substances  will 
be  urged  from  places  where  the  magnetic  force  is  strong 
to  places  where  it  is  weaker. 
This  is  why  a  ball  of  bismuth 
moves  away  from  a   magnet, 
and  why  a  little  bar  of  bismuth 
between  the   conical  poles  of 
the  electromagnet  (Fig.  182) 
turns  equatorially  so  as  to  put 
riff.  1S4.  its  ends  into  the  regions  that 

are  magnetically  weaker.  There  is  no  reason  to  doubt 
that  in  a  magnetic  field  of  uniform  strength  a  bar  of 
bismuth  would  point  along  the  lines  of  induction. 

373.  Magne-Crystallic  Action.  — In  1822  Poisson  pre- 
dicted that  a  body  possessing  crystalline  structure  would, 
if  magnetic  at  all,  have  different  magnetic  powers  in 
different  directions.  In  1847  Pliicker  discovered  that  a 
piece  of  tourmaline,  which  is  itself  feebly  paramagnetic, 
behaved  as  a  diamagnetic  body  when  so  hung  that  the 
axis  of  the  crystal  was  horizontal.  Faraday,  repeating 
the  experiment  with  a  crystal  of  bismuth,  found  that  it 
tended  to  point  with  its  axis  of  crystallization  along  the 
lines  of  the  field  axially.  The  magnetic  force  acting  thus 
upon  crystals  by  virtue  of  their  possessing  a  certain 
structure  he  named  mayne-crystallic  force.  Pliicker  en- 
deavoured to  connect  the  magne-crystallic  behaviour  of 
crystals  with  their  optical  behaviour,  giving  the  following 


368  ELECTRICITY   AND   MAGNETISM      PART  n 

law :  there  will  be  either  repulsion  or  attraction  of  the 
optic  axis  (or,  in  the  case  of  bi-axial  crystals,  of  both  optic 
axes)  by  the  poles  of  a  magnet;  and  if  the  crystal  is  a 
"negative"  one  (i.e.  optically  negative,  having  an  extra- 
ordinary index  of  refraction  less  than  its  ordinary  index) 
there  will  be  repulsion,  if  a  "  positive  "  one  there  will  be 
attraction.  Tyndall  has  endeavoured  to  show  that  this 
law  is  insufficient  in  not  taking  into  account  the  para- 
magnetic or  diamagnetic  powers  of  the  substance  as  a 
whole.  He  finds  that  the  magne-crystallic  axis  of  bodies 
is  in  general  an  axis  of  greatest  density,  and  that  if  the 
mass  itself  be  paramagnetic  this  axis  will  point  axially ;  if 
diamagnetic,  equatorially.  In  bodies  which,  like  slate  and 
many  crystals,  possess  cleavage,  the  planes  of  cleavage 
are  usually  at  right  angles  to  the  magne-crystallic  axis. 
Another  way  of  stating  the  facts  is  to  say  that  in  non- 
isotropic  bodies  the  induced  magnetic  lines  do  not  nec- 
essarily run  in  the  same  direction  as  the  lines  of  the 
impressed  magnetic  field. 

374.  Diamagnetism  of  Flames.  —  In  1847  Bancalari 
discovered  that  flames  are  repelled  from  the  axial  line 
joining  the  poles  of  an  electromagnet.  Faraday  showed 
that  all  kinds  of  flames,  as  well  as  ascending  streams  of 
hot  air  and  of  smoke,  are  acted  on  by  the  magnet,  and 
tend  to  move  from  places  where  the  magnetic  forces  are 
strong  to  those  where  they  are  weaker.  Gases  (except 
oxygen  and  ozone),  and  hot  gases  especially,  are  feebly 
diamagnetic.  But  the  active  repulsion  and  turning  aside 
of  flames  may  possibly  be  in  part  due  to  an  electromag- 
netic action  like  that  which  the  magnet  exercises  on  the 
convexion-current  of  the  voltaic  arc  (Art.  448)  and  on 
other  convexion-currents.  The  electric  properties  of 
flame  are  mentioned  in  Arts.  8  and  314. 


CHAP,  v  THE   MAGNETIC   CIRCUIT  369 


LESSON  XXX.  —  The  Magnetic  Circuit 

375.  Magnetic  Circuits.  —  It  is  now  generally  recog- 
nized that  there  is  a  magnetic  circuit  law  similar  to  the 
law   of  Ohm  for  electric   circuits.      Ritchie,   Sturgeon, 
Joule,  and  Faraday  dimly  recognized  it.      But  the  law 
was  first  put  into  shape  in  1873  by  Rowland,  who  calcu- 
lated the  flow  of  magnetic  lines  through  a  bar  by  dividing 
the  "  magnetizing  force  of  the  helix  "  by  the  "  resistance 
to  lines  of  force  "  of  the  iron.     In  1882  Bosanquet  intro- 
duced the  term  magnetomotive-force,  and  showed  how  to 
calculate  the  reluctances  of  the  separate  parts  of  the  mag- 
netic circuit,  and,  by  adding  them,  to  obtain  the  total 
reluctance.* 

The  law  of  the  magnetic  circuit  may  be   stated  as 
follows :  — 

Magnetic  Flux  =  magnetomotive-force, 
reluctance 

orH=|. 

376.  Reluctance.  —  As  the  electric  resistance  of  a 
prismatic  conductor  can  be  calculated  from  its  length, 
cross-section,  and  conductivity,  so  the  magnetic  reluctance 
of  a  bar  of  iron  can  be  calculated  from  its  length,  cross- 
section,  and  permeability.     The  principal  difference  be- 
tween the  two  cases  lies  in  the  circumstance  that  whilst 
in  the  electric  case  the  conductivity  is  the  same  for  small 
and  large  currents,  in  the  magnetic  case  the  permeability 
is  not  constant,  but  is  less  for  large  magnetic  fluxes  than 
for  small  ones. 

Let  the  length  of  the  bar  be  I  centirns.,  its  section  A 
sq.  cms.,   and  its  permeability  p.     Then  its  reluctance 

*  This  useful  term,  far  preferable  to  "  magnetic  resistance,"  was  intro- 
duced by  Oliver  Heaviside.    The  twin  reluctivity  is  sometimes  used  for 
the  specific  reluctance  ;  it  is  the  reciprocal  of  permeability. 
2B 


370 


ELECTRICITY  AND   MAGNETISM      PART  n 


will  be  proportional  directly  to  /,  and  inversely  to  A  and 
/x.     Calling  the  reluctance  Z  we  have 

Z  = 


Example.  —  An  iron  bar  100  cm.  long  and  4  sq.  cms.  in 
cross-section  is  magnetized  to  such  a  degree  that  ^  =  320: 
then  Z  will  be  0'078. 

The  reluctance  of  a  magnetic  circuit  is  generally  made 
up  of  a  number  of  reluctances  in  series.  We  will  first 
take  the  case  of  a  closed  magnetic  circuit  (Fig.  185)  made 
up  of  a  curved  iron  core  of  length  lv  section  A},  and 
permeability  /XL;  and  an  armature  of 
length  /2,  section  A2,  and  permeability  ju,2, 
in  contact  with  the  ends  of  the  former. 
In  this  case  the  reluctance  is 


Fig.  185. 


377-  Calculation  of  Exciting  Power.  — 
Passing  on  to  the  more  difficult  case  of 
a  circuit  made  up  partly  of  iron  and  partly  of  air,  we 
will  suppose  the  armature  to  be  moved  to  a  distance, 
so  that  there  are  two  air-gaps  in  the  circuit,  each  gap 
of  length  13  (from  iron  to  iron),  and  sec- 
tion A3  (equal  to  area  of  pole  face). 
This  will  introduce  an  additional  reluc- 
tance 2/3/A3,  the  permeability  for  air 
being  =  1.  It  will  also  have  the  effect  of 
making  part  of  the  magnetic  flux  leak 
out  of  the  circuit. 

By  Art.  341,  if  the  exciting  power 
consists  of  C  amperes  circulating  in  S 
spirals  around  the  core,  the  magneto- 
motive-force will  be  47rCS/10.  Applying 
this  to  the  preceding  example,  dividing  the  magneto- 
motive-force by  the  reluctance,  we  get  for  the  magnetic 
flux  — 


Fig.  18C. 


CHAP,  v      CALCULATION  OF   EXCITATION  371 


47TCS 


But  more  often  the  calculation  is  wanted  the  other 
way  round,  to  find  how  many  ampere-turns  of  excitation 
will  be  needed  to  produce  a  given  flux  through  a  magnetic 
circuit  of  given  size.  Two  difficulties  arise  here.  The 
permeability  will  depend  on  the  degree  of  saturation. 
Also  the  leakage  introduces  an  error.  To  meet  the  first 
difficulty  approximate  values  of  /x,  must  be  found.  Sup- 
pose, for  example,  it  was  intended  to  produce  a  flux  of 
1,000,000  lines  through  an  iron  bar  having  a  section  of 
80  sq.  centims.,  then  B  will  be  12,500,  and  reference  to 
the  table  in  Art.  364  shows  that  if  the  bar  is  of  wrought 
iron  fji  will  be  about  1247.  To  meet  the  second  difficulty 
we  must  estimate  (from  experience)  an  allowance  for 
leakage.  Suppose  we  find  that  of  all  the  lines  created  in 
the  U-shaped  part  only  the  fraction  1/v  gets  through 
the  armature,  then  to  force  N  lines  through  the  armature 
we  must  generate  i/N  lines  in  the  U-shaped  piece,  where 
v  is  the  coefficient  of  allowance  for  leakage,  an  improper 
fraction  increasing  with  the  width  of  the  gaps. 

We  then  proceed  to  calculate  in  parts  as  follows  :  — 

Ampere-turns  needed  to  drive  N  lines  1  _  jj  x    ^i      _._  i  .0-7 
through  iron  of  armature.  J 


Ampere-turns  needed  to  drive  N  lines  )      N     2k      ^-,  .9»7 
through  two  gaps.  I  A8 

Ampere-turns  needed  to  drive  vN  lines  J  _   «•  x     h   _._  i  .057 
through  iron  of  magnet  core.  J  ~~  A2/u2 

Then  adding  up,  we  get  :  — 

Total  ampere-turns  needed  =  N  (  -A-  +  -^-  +  ^  I  -=-  1'257. 

I  A^i     A2M2      A3  J 


Formulae  similar  to  this  have  been  used  by  Hopkinson 
and  by  Kapp  in  designing  electromagnets  for  dynamos. 
378.   Effect  of  Air-Gap  in  Circuit.  —  Air  having  no 


372  ELECTRICITY  AND   MAGNETISM      PART  11 

remanence  the  presence  of  a  gap  in  the  iron  circuit  tends 
to  make  residual  magnetism  unstable,  as  though  the 
polar  magnetism  on  the  end-faces  had  a  self-demagnetiz- 
ing effect.  In  fact  it  is  very  difficult  to  give  a  permanent 
magnetism  to  short  pieces  of  metal.  Further,  the  low 
permeability  of  air  necessitates  enormous  magnetomotive- 
forces,  compared  with  those  required  for  iron,  to  produce 
a  given  flux.  The  effect  is  to  shear  over  to  the  right  the 
curves  of  magnetization,  seeing  that  a  greater  H  is  needed 
to  attain  an  equal  value  of  B.  Joints  in  the  magnetic 
circuit  have  the  same  kind  of  effect. 

The  reason  why  the  pull  exerted  by  an  electromagnet 
on  its  armature  falls  off  so  very  greatly  when  the  arma- 
ture is  moved  away  to  a  short  distance  is  the  diminution 
of  the  magnetic  flux  caused  by  the  great  reluctance  of 
the  air-gap  thus  introduced  into  the  circuit. 

379.  General  Law  of  Electromagnetic  Systems.  — 
Consider  an  electromagnetic  system  consisting  of  any 
number  of  parts  —  iron  masses,  coils  carrying  currents, 
air,  masses  of  other  materials,  whether  magnetic  or 
diamagnetic  —  in  any  given  configuration.  Any  change 
in  the  configuration  of  the  parts  will  in  general  produce 
either  an  increase  or  a  decrease  in  the  magnetic  flux.  For 
example,  if  the  armature  of  an  electromagnet  is  allowed 
to  move  up  toward  the  poles,  or  the  needle  of  a  galvano- 
meter is  allowed  to  turn,  there  will  be  a  betterment  of 
the  magnetic  circuit,  and  the  magnetic  flux  through  the 
coils  will  be  increased.  Magnetic  circuits  always  tend  to 
close  up  and  become  as  compact  as  possible.  On  the  con- 
trary, if  we  pull  away  the  armature  from  an  electromag- 
net the  magnetic  reluctance  is  increased,  and  the  flux 
diminished ;  and  this  action  is  resisted  by  the  reaction  of 
the  system.  All  these  things  may  be  summed  up  in  the 
following  general  law  :  — 

Every  electromagnetic  system  tends  so  to  change  the  con- 
figuration of  its  parts  as  to  make  the  magnetic  flux  a 
maximum. 


CHAP,  v          LAW  OF  ELECTROMAGNET  373 

Suppose  (the  external  magnetizing  forces  remaining 
the  same)  a  motion  of  any  part  through  a  distance  dx 
results  in  a  decrease  of  flux  rfN,  then  the  force  resisting 
such  motion  will  be  proportional  to  dW/dx. 

38O.  Law  of  the  Electromagnet.  —  Before  the  law  of  the 
magnetic  circuit  was  understood  many  attempts  were  made  to 
find  algebraic  formulae  to  express  the  relation  between  the 
strength  of  current  and  the  amount  of  magnetism  produced. 
Lenz  and  Jacob!  suggested  that  the  magnetism  of  an  electro- 
magnet ivas  proportional  to  the  current  and  to  the  number  of 
turns  of  wire  in  the  coil  —  in  other  words,  is  proportional  to  the 
ampere-turns.  Or  in  symbols 

m  =  «CS, 

where  a  is  a  constant  depending  on  the  quantity,  quality,  and 
form  of  iron.  This  rule  is,  however,  only  true  when  the  iron 
core  is  still  far  from  being  "  saturated."  If  the  iron  is  already 
strongly  magnetized  a  current  twice  as  strong  will  not  double 
the  magnetization  in  the  iron,  as  Joule  showed  in  1847. 

Miiller  gave  the  following  approximate  rule: —  The  strength 
of  an  electromagnet  is  proportional  to  the  angle  whose  tangent 
is  the  strength  of  the  magnetizing  current ;  or 

m  =  A  tan-iC, 

where  C  is  the  magnetizing  current,  and  A  a  constant  depend- 
ing on  the  construction  of  the  particular  magnet.  If  the  student 
will  look  at  Fig.  121  and  imagine  the  divisions  of  the  horizontal 
tangent  line  OT  to  represent  strengths  of  current,  and  the 
number  of  degrees  of  arc  intercepted  by  the  oblique  lines  to 
represent  strengths  of  magnetism,  he  will  see  that  even  if  OT  be 
made  infinitely  long,  the  intercepted  angle  can  never  exceed  90°. 
Another  formula,  known  as  Frolich's,  is  — 


'    1+60' 

where  a  and  b  are  constants  depending  on  the  form,  quality,  and 
quantity  of  the  iron,  and  on  the  winding  of  the  coil.  The  con- 
stant b  is  the  reciprocal  of  that  number  of  amperes  which  would 
make  m  equal  to  half  possible  maximum  of  magnetism. 

The  author's  variety  of  this  formula  expresses  the  number  of 
magnetic  lines  N  proceeding  from  the  pole  of  the  electromagnet  — 


374 


ELECTRICITY   AND   MAGNETISM      PART  n 


where  Y  represents  the  maximum  number  of  magnetic  lines  that 
there  would  he  if  the  magnetizing  current  were  indefinitely  in- 
creased and  the  iron  core  saturated,  and  C'  stands  for  that  number 
of  amperes  which  would  bring  the  magnetism  up  to  half-satura- 
tion. 

None  of  these  empirical  formulas  are  as  useful  as  the  rational 
formula  at  the  end  of  Art.  377. 


LESSON  XXXI.  —  Electromagnets 

381.  Electromagnets.  —  In  1820,  almost  immediately 
after  Oersted's  discovery  of  the  action  of  the  electric  cur- 
rent on  a  magnet  needle,  Arago  and  Davy  independently 
discovered  how  to  magnetize  iron  and  steel  by  inserting 
needles  or  strips  into  spiral  coils  of  copper  wire  around 


Fig.  187 


which  a  current  was  circulating.  The  method  is  shown 
in  the  simple  diagram  of  Fig.  187,  where  a  current  from 
a  single  cell  is  passed  through  a  spiral  coil  of  insulated 
copper  wire,  in  the  hollow  of  which  is  placed  a  strip  of 
iron  or  steel,  which  is  thereby  magnetized.  The  separate 
turns  of  the  coil  must  not  touch  one  another  or  the 
central  bar,  otherwise  the  current  will  take  the  shortest 
road  open  to  it  and  will  not  traverse  the  whole  of  the 
coils.  To  prevent  such  short-circuiting  by  contact  the 


STURGEON'S   ELECTROMAGNET 


wire  of  the  coil  should  be  overspun  with  silk  or  cotton 
(in  the  latter  case  insulation  is  improved  by  varnishing  it 
or  by  steeping  the  cotton  covering  in  melted  paraffin  wax), 
or  covered  with  a  layer  of  guttapercha.  If  the  bar  be  of 
iron  it  will  be  a  magnet  only  so  long  as  the  current  flows; 
and  an  iron  bar  thus  surrounded  with  a  coil  of  wire  for 
the  purpose  of  magnetizing  it  by  an  electric  current  is 
called  an  Electromagnet.  Sturgeon,  who  gave  this  name, 
applied  the  discoveries  of  Davy  and  Arago  to  the  con- 
struction of  electromagnets  far  more  power- 
ful than  any  magnets  previously  made. 
His  first  electromagnet  was  a  horse-shoe 
(Fig.  188)  made  of  a  rod  of  iron  about 
1  foot  long  and  ^  inch  in  diameter 
coiled  with  a  single  stout  copper  wire 
of  only  18  turns.  With  the  current  from 
a  single  cell  it  lifted  9  Ibs. ;  but  with  a 
more  powerful  battery  it  lifted  50  Ibs.  It 
was  first  shown  by  Henry  that  when  electromagnets  are 
required  to  work  at  the  distant  end  of  a  long  line  they 
must  be  wound  with  many  turns  of  fine  wire.  The 
great  usefulness  of  the  electromagnet  in  its  application 
to  electric  bells  and  telegraphic  instruments  lies  in  the 
fact  that  its  magnetism  is  under  the  control  of  the  current; 
when  circuit  is  "made"  it  becomes  a  magnet,  when 
circuit  is  "  broken  "  it  ceases  to  act  as  a  magnet.  More- 
over, it  is  capable  of  being  controlled  from  a  distance,  the 
current  being  "  made  "  or  "  broken  "  at  a  distant  point  of 
the  circuit  by  a  suitable  key  or  "switch." 

382.  Polarity  and  Circulation  of  Current.  —  By  apply- 
ing Ampere's  Rule  (Art.  197)  we  can  find  which  end  of 
an  electromagnet  will  be  the  N-seeking  pole ;  for,  imagin- 
ing ourselves  to  be  swimming  in  the  current  (Fig.  187), 
and  to  face  towards  the  centre  where  the  iron  bar 
is,  the  N-seeking  pole  will  be  on  the  left.  It  is  con- 
venient to  remember  this  relation  by  the  following  rules  : 
—  Looking  at  the  S-seeking  pole  of  an  electromagnet,  the 


376 


ELECTRICITY   AND   MAGNETISM      PART  n 


magnetizing  currents  are  circulating  round  it  in  the  same 
cyclic  direction  as  the  hands  of  a  clock  move ;  and,  looking 
at  the  N-seeking  pole  of  an  electromagnet,  the  magnetizing 
currents  are  circulating  round  it  in  the  opposite  cyclic 
direction  to  that  of  the  hands 
of  a  clock.  Fig.  189  shows 
this  graphically.  These  rules 
are  true,  no  matter  whether 
Vv  -— </  the  beginning  of  the  coils  is 
Fig,  189  at  the  end  near  the  observer, 

or  at  the   farther  end   from 

him,  i.e.  whether  the  spiral  be  a  right-handed  screw,  or 
(as  in  Fig.  187)  a  left-handed  screw.  It  will  be  just  the 
same  thing,  so  far  as  the  magnetizing  power  is  concerned, 
if  the  coils  begin  at  one  end  and  run  to  the  other  and 
back  to  where  they  began ;  or  they 
may  begin  half-way  along  the  bar  and 
run  to  one  end  and  then  back  to  the 
other:  the  one  important  thing  to 
know  is  which  way  the  current  flows 
round  the  bar  when  you  look  at  it 
end-on.  The  corkscrew  rule  (Art. 
198)  leads  to  the  same  result. 

Suppose  an  iron  core  to  be  wound 
with  a  right-handed  coil,  and  that  a 
current  is  introduced  at  some  point, 
and  to  flow  both  ways,  it  will  produce 
oppositely-directed  magnetizing  actions  in  the  two  points, 
and  there  will  be  consequent  poles  (Art.  120)  at  the  point 
of  entrance.  In  Fig.  190  an  iron  ring  with  a  right- 
handedly  wound  closed  coil  is  shown.  There  will  be  a 
double  S  pole  at  the  point  where  the  current  enters,  and 
a  double  N  pole  where  it  leaves  the  windings. 

383.  Construction  of  Electromagnets.  —  The  most 
useful  form  of  electromagnet  is  that  in  which  the  iron 
core  is  bent  into  the  form  of  a  horse-shoe,  so  that  both 
poles  may  be  applied  to  one  iron  armature.  In  this 


Fig.  190. 


CHAP,  v       FORMS  OF  ELECTROMAGNETS 


377 


case  it  is  usual  to  divide  the  coils  into  two  parts  wound 
on  bobbins,  as  in  Figs.  64  and  191.  The  electromagnet 
depicted  in  Fig.  192  is  of  a  form  adapted  for  laboratory 
experiments,  and  has  movable  coils  which  are  slipped  on 
over  the  iron  cores.  The  cores  are  united  at  the  bottom 
by  a  stout  iron  yoke.  Sometimes  only  one  coil  is  wound 
on  the  yoke  part.  A  special 
form  of  electromagnet  de- 
vised by  Ruhmkorft'  for  ex- 
periments on  diamagnetism 
is  shown  in  Fig.  182. 

Many  special  forms*  of 
electromagnet  have  been  de- 
vised for  special  purposes. 
To  give  a  very  powerful 
attraction  at  very  short  dis- 
tances, a  short  cylindrical 
electromagnet  surrounded  by 
an  outer  iron  tube,  united  at 
the  bottom  by  iron  to  the  iron  core,  is  found  best;  the 
iron  jacket  constituting  a  return  path  for  the  magnetic 
lines.  This  form  is  known  as  an  iron-clad  magnet.  To 
attract  iron  across  a  wide  gap  which  offers  much  reluc- 
tance, a  horse-shoe  shape  with  long  cores  should  be  chosen  ; 
for  it  needs  long  cores  to  wind  on  enough  wire  to  provide 
sufficient  exciting  power  to  drive  the  flux  across  the  gap. 
To  give  a  gentle  pull  over  a  long  range  a  solenoid  (Art. 
385),  or  long  tubular  coil,  having  a  long  movable  iron  core 
is  used.  For  giving  a  very  quick-acting  magnet  the  coils 
should  not  be  wound  all  along  the  iron,  but  only  round 
the  poles.  As  a  rule  the  iron  parts,  including  the  yoke 
and  armature,  should  form  as  nearly  as  possible  a  closed 
magnetic  circuit.  The  cross-sections  of  yokes  should  be 
thicker  than  those  of  the  cores. 


Fig-.  191. 


*  For  descriptions  of  these,  as  well  as  for  discussion  of  all  other  matters 
relating  to  the  subject,  see  the  author's  treatise  on  The  Electromagnet  and 
Electromagnetic  Mechanism. 


378 


ELECTRICITY  AND   MAGNETISM        PART  n 


384.  Lifting-power  of  Electromagnets.  —  The  trac- 
tive force  of  an  electromagnet  depends  not  only  on  its 
magnetic  strength,  but  also  upon  its  form,  and  on  the 


shape  of  its  poles,  and  on  the  form  of  the  soft  iron 
armature  which  it  attracts.  It  should  be  so  arranged 
that  as  many  lines  of  force  as  possible  should  run  through 
the  armature,  and  the  armature  itself  should  contain  a 
sufficient  mass  of  iron.  Joule  designed  a  powerful  elec- 
tromagnet, capable  of  supporting  over  a  ton.  The 
maximum  attraction  he  could  produce  between  an  electro- 
magnet and  its  armature  was  200  Ibs.  per  square  inch,  or 
about  13,800,000  dynes  per  square  centimetre.  Bidwell 
has  found  the  attraction  to  go  up  to  226-3  Ibs.  per  square 


CHAP,  v      LAW   OF  MAGNETIC  TRACTION 


379 


inch  when  the  wrought  iron  core  was  saturated  up  to 
19,820  magnetic  lines  to  the  square  centimetre.  The 
law  of  traction  is  that  the  pull  per  square  centimetre  is 
proportional  to  the  square  of  the  number  of  lines  per 
square  centimetre  :  or  in  symbols 


-p 


B2A 


where  P  is  the  pull  in  dynes,  and  A  the  area  in  square 
centims.  In  the  following  table  are  given  the  values  of 
the  tractive  force  for  different  stages  of  magnetization. 


B 

lines  per 
sq.  cm. 

Dynes 
per 
sq.  centim. 

Grammes 
per 
sq.  centim. 

Pounds 
per 
sq.  inch. 

1,000 

39,790 

40-56 

•577 

2,000 

159,200 

162-3 

2-308 

3,000 

358,100 

365-1 

5-190 

4,000 

630,600 

648-9 

9-228 

5,000 

994,700 

1,014 

14-39 

0,000 

1,432,000 

1,460 

20-75 

7,000 

1,950,000 

1,987 

28-26 

8,000 

2,547,000 

2,596 

36-95 

9,000 

3,223,000 

3,286 

46-72 

10,000 

3,979,000 

4,056 

57-68 

12,000 

5,730,000 

5,841 

83-07 

14,000 

7,800,000 

7,950 

113-1 

16,000 

10,170,000 

10,390 

147-7 

18,000 

12,890,000 

13,140 

186*8 

20,000 

15,920,000 

16,230 

230-8 

It  will  be  noted  that  doubling  B  makes  the  pull  four 
times  as  great.  One  curious  consequence  of  this  law  is 
that  to  enlarge  its  poles  weakens  the  pull  of  an  electro- 
magnet or  magnet.  In  some  cases  —  bar  magnets  for 
example  —  their  tractive  power  is  increased  by  filing 
down  or  rounding  the  poles  so  as  to  concentrate  B. 


380  ELECTRICITY   AND   MAGNETISM      PART  n 

385.  Solenoid.  —  Without  any  central  core  of  iron 
or  steel  a  spiral  coil  of  wire  traversed  by  a  current  acts  as 
an  electromagnet  (though  not  so  powerfully  as  when  an 
iron  core  is  placed  in  it).  Such  a  coil  is  sometimes  termed 
a  solenoid.  A  solenoid  has  two  poles  and  a  neutral 
equatorial  region.  Ampere  found  that  it  will  attract 
magnets  and  be  attracted  by  magnets.  It  will  attract 
another  solenoid;  it  has  a  magnetic  field  resembling 

generally  that  of  a 
bar   magnet.     If  so 
arranged  that  it  can 
turn  round   a  verti- 
cal  axis,  it  will  set 
itself    in    a    North 
and  South  direction 
\'f)j     along  the   magnetic 
meridian.     Fig.  193 
shows  a  solenoid  ar- 
ranged with  pivots,  by  which  it  can  be  suspended  to  a 
"table,"  like  that  shown  in  Fig.  198. 

With  an  iron  core  the  solenoid  becomes  far  more 
powerful.  The  effect  of  the  iron  core  is  by  its  greater 
permeability  to  multiply  the  number  of  magnetic  lines 
as  well  as  to  concentrate  them  at  definite  poles.  The 
student  has  been  told  (Art.  202)  that  the  lines  of  force  due 
to  a  current  flowing  in  a  wire  are  closed  curves,  approxi- 
mately circles  (Figs.  115  and  195),  round  the  wire.  If 
there  were  no  iron  core  many  of  these  little  circular  lines 
of  force  would  simply  remain  as  small  closed  curves 
around  their  own  wire ;  but,  since  iron  has  a  permeability 
hundreds  of  times  greater  than  air,  wherever  the  wire 
passes  near  an  iron  core  the  magnetic  lines  alter  their  shape, 
and  instead  of  being  little  circles  around  the  separate 
wires,  run  through  the  iron  core  from  end  to  end,  and 
round  outside  from  one  end  of  the  coil  back  to  the  other. 
A  few  of  the  magnetic  lines  do  this  when  there  is  no  iron  ; 
almost  all  of  them  do  this  when  there  is  iron,  and  when 


CHAP,  v  FIELD  INSIDE   SOLENOID  381 

there  is  iron  there  are  more  lines  to  flow  back.*  Hence 
the  electromagnet  with  its  iron  core  has  enormously 
stronger  poles  than  the  spiral  coils  of  the  circuit  would 
have  alone. 

In  Art.  342  it  was  shown  that  the  intensity  of  the 
magnetic  field  down  the  middle  of  a  solenoid  of  length  /, 
having  S  spirals,  carrying  C  amperes,  is  — 


Since  the  area  enclosed  is  irr2,  the  flux  down  the 
solenoid  (without  iron)  will  be 


And,  since  4?r  magnetic  lines  go  to  one  unit  of  mag- 
netism, the  solenoid  (without  iron)  will  act  as  though 
it  had  as  the  magnetism  at  its  pole  — 


10/ 

It  will  be  noticed  that  for  any  solenoid  of  given  length 
and  radius  the  three  magnetic  quantities  H  (internal 
field),  N  (magnetic  flux),  and  m  (strength  of  poles)  are 
proportional  to  the  amperes  of  current  and  to  the  number 
of  turns  in  the  coil.  The  product  which  thus  comes 
into  all  electromagnet  formulae  is  called  the  number  of 
ampere-turns. 

A  solenoid  with  a  movable  iron  plunger  is  sometimes 
called  a  sucking-magnet.  The  iron  core  tends  to  move  into 
the  position  in  which  it  best  completes  (Art.  379)  the 
magnetic  circuit.  If  the  core  is  much  longer  than  the 
coil,  the  pull  increases  as  the  end  of  the  core  penetrates 

*  But,  in  the  case  of  a  permanent  steel  horse-shoe  magnet,  bringing  up 
the  iron  keeper,  though  it  concentrates  the  lines  through  the  poles,  does 
not  increase  the  total  number  of  lines  through  the  bend  of  the  U. 


382  ELECTRICITY   AND   MAGNETISM      PART  n 

down  the  coil,  diminishing  quickly  as  the  core  emerges. 
Short  iron  cores  are  only  pulled  while  at  the  mouth  of 
the  coil ;  the  maximum  pull  being  when  about  half  their 
length  has  entered. 

386.  The  Winding  of  Electromagnets.  —  The  exact 
laws  governing  the  winding  of  electromagnets  are  some- 
what complicated;  but  it  is  easy  to  give  certain  rules 
which  are  approximately  true.  Every  electromagnet 
shows  the  same  general  set  of  facts  —  that  with  small 
exciting  power  there  is  little  magnetism  produced,  with 
larger  exciting  power  there  is  more  magnetism,  and  that 
with  very  great  exciting  power  the  iron  becomes  prac- 
tically saturated  and  will  take  up  very  little  additional 
magnetism.  It  follows  at  once  that  if  the  electromagnet 
is  destined  to  be  used  at  the  end  of  a  long  line  through 
which  only  a  small  current  (perhaps  only  yi¥  ampere) 
will  flow,  the  requisite  number  of  ampere-turns  to  excite 
the  magnetism  will  not  be  attained  unless  many  turns  of 
wire  are  used;  and  as  the  current  is  small  a  fine  wire 
may  be  used. 

It  may  be  noted  that  when  electromagnets  are  wound 
with  many  turns  of  fine  wire,  these  coils  will  add  to  the 
electric  resistance  of  the  circuit,  and  will  tend  to  diminish 
the  current.  Herein  lies  a  difference  in  construction  of 
telegraphic  and  other  instruments;  for  while  electro- 
magnets with  "  long  coils,"  consisting  of  many  turns  of 
fine  wire,  must  be  used  on  long  circuits  where  there  is 
great  line  resistance,  such  an  instrument  would  be  of  no 
service  in  a  laboratory  circuit  of  very  small  resistance, 
for  the  resistance  of  a  long  thin  coil  would  be  dispro- 
portionately great:  here  a  short  coil  of  few  turns  of 
stout  wire  would  be  appropriate  (see  Art.  192). 

It  is  the  nature  of  the  line,  according  to  whether  it  is 
of  high  resistance  or  low,  which  governs  the  questions 
how  the  coil  shall  be  wound  and  how  the  battery  shall 
be  grouped. 

Similar  electromagnets  of   different  sizes  must  have 


CHAP,  v     WINDING   OF   ELECTROMAGNETS  383 

ampere-turns  proportional  to  their  linear  dimensions  if 
they  are  to  be  raised  to  equal  degree  of  saturation. 

As  the  magnetism  of  the  magnet  depends  on  the 
number  of  ampere-turns,  it  should  make  no  matter 
whether  the  coils  are  bigger  than  the  core  or  whether 
they  enwrap  it  quite  closely.  If  there  were  no  magnetic 
leakage  this  would  be  true  in  one  sense ;  but  for  an  equal 
number  of  turns  large  coils  cost  more  and  offer  higher  re- 
sistance. Hence  the  coils  are  wound  as  closely  to  the  iron 
core  as  is  consistent  with  good  insulation.  Also  the  iron 
is  chosen  as  thick  as  possible,  as  permeable  as  possible, 
and  forming  as  compact  a  magnetic  circuit  as  possible,  so 
that  the  magnetic  resistance  may  be  reduced  to  its  utmost, 
giving  the  greatest  amount  of  magnetism  for  the  number 
of  ampere-turns  of  excitation.  This  is  why  horse-shoe- 
shaped  electromagnets  are  more  powerful  than  straight 
electromagnets  of  equal  weight;  and  why  also  a  horse- 
shoe electromagnet  will  only  lift  about  a  quarter  as  much 
load  if  one  pole  only  is  used  instead  of  both. 

As  the  coils  of  electromagnets  grow  hot  with  the 
current,  sufficient  cooling  surface  must  be  allowed,  or 
they  may  char  their  insulation.  Each  square  centimetre 
of  surface  warmed  1°  C.  above  the  surrounding  air  can 
get  rid  of  about  0-0029  watt.  If  50°  above  the  sur- 
rounding air  be  taken  as  the  safe  limit  of  rise  of  tem- 
perature, and  the  electromagnet  has  resistance  r  and 
surface  s  sq.  cms.,  the  highest  permissible  current  will  be 
0-38  Vs/r  amperes. 

387.  Polarized  Mechanism.  —  An  electromagnet 
moves  its  armature  one  way,  no  matter  which  way  the 
current  flows.  Reversing  the  current  makes  no  difference. 
There  are,  however,  two  ways  of  making  a  mechanism 
that  will  cause  an  armature  to  move  in  either  sense  at 
will,  (a)  The  armature's  movement  is  controlled  by 
an  adjusted  spring  so  as  to  be  in  an  intermediate  position 
when  a  weak  current  is  flowing.  Then  sending  a  stronger 
current  will  move  the  armature  one  way,  and  weakening 


384  ELECTRICITY   AND   MAGNETISM      PAHT  n 

or  stopping  the  current  will  make  it  move  the  other  way. 
(b)  A  polarized  armature  or  tongue  (i.e.  one  that  is  in- 
dependently magnetized)  is  placed  between  the  poles  of  the 
electromagnet  instead  of  opposite  them.  The  direction 
in  which  it  tends  to  move  will  be  reversed  by  reversing 
the  current  in  the  circuit  of  the  electromagnet. 

388.  Growth  of  Magnetism.  —  It  requires  time  to 
magnetize  an  iron  core.  This  is  mainly  due  to  the  fact 
that  a  current,  when  first  switched  on,  does  not  instantly 
attain  its  full  strength,  being  retarded  by  the  self-induced 
counter-electromotive-force  (Art.  458)  ;  it  is  partly  due  to 
the  presence  of  transient  reverse  eddy-currents  (Art.  457) 
induced  in  the  iron  itself.  Faraday's  large  electromagnet 
at  the  Royal  Institution  takes  about  two  seconds  to  attain 
its  maximum  strength.  The  electromagnets  of  large 
dynamo  machines  often  take  ten  minutes  or  more  to  rise 
to  their  working  stage  of  magnetization. 

When  electromagnets  are  used  with  rapidly  alternating 
currents  (Art.  470)  there  are  various  different  pheno- 
mena, for  which  the  student  is  referred  to  Art.  477. 


LESSON  XXXII.  —  Electrodynamics 

389.  Electrodynamics.  —  In  1821,  almost  immedi- 
ately after  Oersted's  discovery  of  the  action  of  a  current 
on  a  magnet,  Ampere  discovered  that  a  current  acts  upon 
another  current,  apparently  attracting  it  *  or  repelling  it 
according  to  certain  definite  laws.  These  actions  he  in- 
vestigated by  experiment,  and  from  the  experiments  he 
built  up  a  theory  of  the  force  exerted  by  one  current  on 
another.  That  part  of  the  science  which  is  concerned 
with  the  force  which  one  current  exerts  upon  another 
he  termed  Electrodynamics.  It  is  now  known  that  these 

*  It  would  be  more  correct  to  speak  of  the  force  as  acting  on  conductors 
carrying  currents,  than  as  acting  ou  the  currents  themselves. 


CHAP,  v    MAGNETIC  FIELD  AROUND  CURRENTS    385 


actions  are  purely  magnetic,  and  are  due  to  stresses  in  the 
intervening  medium.  The  magnetic  field  around  a  single 
conductor  consists  of  a  magnetic  whirl  (Art.  202),  and 
any  other  conductor  carrying  a  current  when  brought 
into  the  field  of  the  first  is  acted  upon  by  it.  Fig.  194 
shows  the  field  due  to  two  parallel  straight  current  con- 


Fig.  194. 


ductors,  which  were  passed  through  holes  in  a  sheet  of 
glass  on  which  iron  filings  were  sprinkled.  In  Fig.  194 
the  currents  flow  in  the  same  direction ;  in  Fig.  195  in 
opposite  directions.  In  the  first  case  the  stresses  in  the 
field  (Art.  119)  tend  to  pull  them  together,  in  the  second 
to  push  them  apart.* 

39O.  Laws  of  Parallel  and  Oblique  Circuits.  —  The 
following  are  the  laws  discovered  by  Ampere :  — 

(i.)  Two  parallel  portions  of  a  circuit  attract  one  another 
if  the  currents  in  them  are  flowing  in  the  same  direction,  and 
repel  one  another  if  the  currents  flow  in  opposite  directions. 

This  law  is  true  whether  the  parallel  wires  be  parts  of 
two  different  circuits  or  parts  of  the  same  circuit. 
The  separate  turns  of  a  spiral  coil,  like  Fig.  193, 
when  traversed  by  a  current  attract  one  another ; 
such  a  coil,  therefore,  shortens  when  a  current  is 
sent  through  it.  But  this  is  equally  well  explained 

*  See  article  by  the  author  in  the  Philosophical  Magazine,  November 
1878,  p.  348. 

2o 


386 


ELECTRICITY   AND   MAGNETISM      PART  ii 


by  the  general  law  '6f  electromagnetic  systems 
(Art.  379),  because  shortening  will  reduce  the 
reluctance  of  the  magnetic  circuit  and  increase 
the  flux. 

(ii . )  Two  portions  of  circuits  crossing  one  another  obliquely 
attract  one  another  if  both  the  currents  run  either  towards  or 
from  the  point  of  crossing,  and  repel  one  another  if  one  runs 
to  and  the  other  from  that  point. 

Fig.  196  gives  three  cases  of  attraction  and  two  of  re- 
pulsion that  occur  in  these  laws. 

(iii.)  When  an  element  of  a  circuit  exerts  a  force  on 
another  element  of  a  circuit,  that  force  always  tends  to  urge 


Fig.  196. 

the  latter  in  a  direction  at  right  angles  to  its  own  direction. 

Thus,  in  the  case  of  two  parallel  circuits,  the  force  of 

attraction  or  repulsion  acts  at  right  angles  to  the  currents 

themselves. 

An  example  of  laws  ii.  and  iii.  is  afforded  by  the  case 
shown  in  Fig.  197.  Here  two  currents  ab  and  cd 
are  movable  round  O  as  a  centre.  There  will  be 
an  apparent  repulsion  between  a  and  d  and  be- 
tween c  and  b,  while  in  the  other  quadrants  there 
will  be  an  apparent  attraction,  a  attracting  c,  and 
b  attracting  d. 


CHAP,  v       ATTRACTIONS   OF  CURRENTS 


387 


The  foregoing   laws   may   be   summed    up   in    one, 

by  saying  that  two  portions  of  circuits,  however 

situated,  set  up  stresses 

in      the      surrounding 

medium  tending  to  set 

them  so  that  their  cur- 

rents flow  as  nearly  in 

the     same     path      as 

possible. 
(iv.)   The  force  exerted  be- 

tween two  parallel  portions  of  circuits  is  proportional  to  the 
product  of  the  strengths  of  the  two  currents,  to  the  length  of 
the  portions,  and  inversely  proportional  to  the  simple  distance 
between  them. 

391.   Ampere's  Table.  —  In  order  to  observe  these 
attractions  and  repulsions,  Ampere  devised  the  piece  of 


Fig  19T 


Fig.  198. 

apparatus  known  as  Ampere's  Table,  shown  in  Fig.  198, 
consisting  of  a  double  supporting  stand,  upon  which 
wires,  shaped  in  different  ways,  can  be  so  hung  as  to  be 
capable  of  rotation.  The  ends  of  the  suspended  wires 


388 


ELECTRICITY    AND   MAGNETISM      PART  n 


dip  into  two  mercury  cups,  so  as  to  ensure  good  contact, 
while  allowing  freedom  to  move. 

By  the  aid  of  this  piece  of  apparatus  Ampere  further 
demonstrated  the  following  points :  — 

(a)  A  circuit  doubled  back  upon  itself,  so  that  the  current 

flows  back  along  a  path  close  to  itself,  exerts  no  force 

upon  external  points. 
(6)  A  circuit  bent  into  zig-zags  or  sinuosities  produces  the 

same  magnetic  effects  on  a  neighbouring  piece  of  circuit 

as  if  it  were  straight. 

(c)  There  is  in  no  case  any  force  tending  to  move  a  conduc- 
tor in  the  direction  of  its  own  length. 

(d)  The  force  between  two  conductors  of  any  form  is  the 
same,  whatever  the  linear  size  of  the  system,  provided 
the  distances  be  increased  in  the  same  proportion,  and 
that  the  currents  remain  the  same  in  strength. 

The  particular  case,  given  in  Fig.  199,  will  show  the  value  of 
these  experiments.  Let  AB  and  CD  represent  two  wires  carry- 
ing currents,  lying  neither  parallel  nor  in  the  same  plane.  It 
follows  from  (6)  that  if  we  replace  the  portion  PQ  by  the  crooked 


Fig.  199. 

wire  PRSQ,  the  force  will  remain  the  same.  The  portion  PR  is 
drawn  vertically  downwards,  and  as  it  can,  by  (c),  experience  no 
force  in  the  direction  of  its  length,  this  portion  will  neither  be 
attracted  nor  repelled  by  CD.  In  the  portion  RS  the  current  runs 
at  right  angles  to  CD,  and  this  portion  is  neither  attracted  nor 
repelled  by  CD.  In  the  portion  SQ  the  current  runs  parallel  to 
CD,  and  in  the  same  direction,  and  will  therefore  be  attracted 
downwards.  On  the  whole  therefore,  PQ  will  be  urged  towards 


CHAP,  v         ELECTRODYNAMIC   THEORY  389 

CD.  The  portions  PR  and  RS  will  experience  forces  of  rotation, 
however,  P  being  urged  round  R  as  a  centre  towards  C,  and  R 
being  urged  horizontally  round  S  towards  C.  These  actions 
would  tend  to  make  AB  parallel  with  CD. 

392.  Ampere's  Theory. — From  the  four  preceding 
experimental  data,  Ampere  built  up  an  elaborate  mathe- 
matical theory,  assuming  that,  in  the  case  of  these  forces 
acting  apparently  at  a  distance  across  empty  space,  the 
action  took  place  in  straight  lines  between  two  points, 
the  total  attraction  being  calculated  as  the  sum  of  the 
separate  attractions  on  all  the  different  parts. 

The  briefest  summary  must  suffice.  If  we  deal  first  with 
two  parallel  elements  of  length  dli  and  dl2  carrying  currents 
CiCs,  and  set  at  right  angles  to  the  distance  r  joining  them, 
their  mutual  force  will  be 

df  =  —  C1C.2dl1dl2/lWr'2. 

If,  however,  they  are  not  parallel  or  in  one  plane,  let  0  be 
the  angle  they  make  with  one  another,  while  ^  and  02  are  the 
angles  they  make  with  r ;  when 

4f=  —  C&dlidl^cos  </>  —  i  cos  0rcos  02)/100>-2. 

By  integrating  this  expression  one  obtains  the  forces  for 
circuits  of  any  given  dimensions.  For  example,  for  two  parallel 
straight  conductors  of  lengths  lil.2,  if  these  lengths  are  great 
compared  with  the  distance  r  between  them,  we  have 

/  =  —  2C1C2Z1/2/100r. 

The  researches  of  Faraday  have,  however,  led  to  other 
views;  the  mutual  attractions  and  repulsions  being  re- 
garded as  due  to  actions  taking  place  in  the  medium 
which  fills  the  space  around  and  between  the  conductors. 
All  these  so-called  electrodynamlc  actions  are  merely 
magnetic  actions. 

An  interesting  experiment,  showing  an  apparent 
mutual  self-repulsion  between  contiguous  portions  of  the 
circuit,  was  devised  by  Ampere.  A  trough  divided  by 
a  partition  into  two  parts,  and  made  of  non-conduct- 
ing materials,  is  filled  with  mercury.  Upon  it  floats  a 


ELECTRICITY  AND    MAGNETISM      PART  n 


metallic  bridge  formed  of  a  bent  wire,  of  the  form  shown 
in  Fig.  200,  or  consisting  of  a  glass  tube  filled  siphonwise 
with  mercury.  When  a  current  is  sent  through  the 


Fig.  200. 

floating  conductor  from  X  over  MN,  and  out  at  Y,  the 
floating  bridge  is  observed  to  move  so  as  to  increase  the 
area  enclosed  by  the  circuit.  But  the  force  would  be 
diminished  indefinitely  if  the  two  parallel 
parts  could  be  made  to  lie  quite  close  to 
one  another. 

393.  Electromagnetic  Rotations.  - 
Continuous  rotation  can  be  produced 
between  a  magnet  and  a  circuit,  or  be- 
tween two  parts  of  one  circuit,  provided 
that  one  part  of  the  circuit  can  move 
while  another  part  remains  fixed,  or  that 
Q  the  current  in  one  part  can  be  reversed. 
The  latter  device  is  adopted  in  the  con- 
struction of  electric  motors  (Art.  443). 
The  former  alternative  is  applied  in 
some  historic  apparatus  for  showing 
rotations,  a  sliding-contact  being  made 
between  one  part  of  the  circuit  and 
Several  different  forms  of  rotation-apparatus 
were  devised  by  Faraday  and  by  Ampere.  One  of 
Faraday's  is  shown  in  Fig.  201,  in  which  a  wire  carrying 
a  current  is  jointed  at  the  top  and  dips  into  a  cup  of 


CHAP,  v  ELECTRODYNAMOMETERS  391 

mercury  surrounding  the  pole  of  a  magnet.  On  switching 
on  the  current  the  wire  at  once  begins  to  walk  round  the 
pole  with  a  motion  that  continues  until  the  current  is 
switched  off. 

A  pole  of  a  magnet  can  also  be  made  to  rotate  round 
a  current ;  and  if  a  vertical  magnet  be  pivoted  so  as  to 
turn  around  its  own  axis  it  will  rotate  when  a  current  is 
led  into  its  middle  region  and  out  at  either  end.  If  the 
current  is  led  in  at  one  end  and  out  at  the  other  there 
will  be  no  rotation,  since  the  two  poles  would  thus  be 
urged  to  rotate  in  opposite  ways.  Liquid  conductors  too 
can  exhibit  electromagnetic  rotations.  Let  a  cylindrical 
metallic  vessel  connected  to  one  pole  of  a  battery  be 
filled  with  mercury  or  dilute  acid,  and  let  a  wire  from 
the  other  pole  dip  into  its  middle,  so  that  a  current  may 
flow  radially  from  the  centre  to  the  circumference,  or 
vice  versa ;  then,  if  this  be  placed  upon  the  pole  of  a 
powerful  magnet,  or  if  a  magnet  be  held  vertically  over 
it,  the  liquid  may  be  seen  to  rotate. 

394.  Electrodynamometer. —  Weber  devised  an  in- 
strument known  as  an  electrodynamometer  for  measuring 
the  strength  of  currents  by  means  of  the  electrodynarnic 
action  of  one  part  of  the  circuit  upon  another  part.  It 
is  a  sort  of  galvanometer,  in  which,  instead  of  a  needle, 
there  is  a  small  coil  suspended.  One  form  of  this  instru- 
ment, in  which  both  the  large  outer  and  small  inner  coils 
consist  of  two  parallel  coils  of  many  turns,  is  shown  in 
Fig.  202.  The  inner  coil  CD  is  suspended  with  its  axis 
at  right  angles  to  that  of  the  outer  coils  AA,  BB,  and  is 
supported  bijilarly  (see  Art.  130)  by  two  fine  metal  wires. 
If  one  current  flows  round  both  coils  in  either  direction  the 
inner  bobbin  tends  to  turn  and  set  its  coils  parallel  to 
the  outer  coils ;  the  sine  of  the  angle  through  which  the 
suspending  wires  are  twisted  being  proportional  to  the 
square  of  the  strength  of  the  current. 

If  G  be  the  "  principal  constant  "  (Art.  213)  of  the  large  coils, 
and  y  the  "  moment  "  of  the  small  coils  (Art.  310)  when  carrying 


392 


ELECTRICITY   AND   MAGNETISM       PART  n 


unit  current,  and  CjC^  the  currents  in  them,  the  torque  (or  turn- 
ing moment)  will  be 


The  chief  advantage  of  this  instrument  over  a  galvan- 
ometer is,  that  it  may  be  used  for  alternating  currents  ;  a 


Fig.  202. 

current  in  one  direction  being  followed  by  a  reverse 
current,  perhaps  thousands  of  times  in  a  minute.  Such 
currents  hardly  affect  a  galvanometer  needle  at  all;  the 
needle  simply  quivers  in  its  place  without  turning. 

395.  Siemens's  Electrodynamometer.  —  In  Siemens's 
dynamometer  (Fig.  203),  much  used  for  measurement 
of  strong  currents,  whether  of  the  continuous  or  the 
alternating  kind,  one  coil  is  fixed  permanently,  whilst 
the  other  coil,  of  one  or  two  turns,  dipping  with  its 
ends  in  mercury  cups,  is  hung  at  right  angles,  and 
controlled  by  a  spiral  spring  below  a  torsion-head. 


CURRENT  BALANCES 


393 


When  current   passes   the    movable   coil   tends   to   turn 
parallel  to  the  fixed  coils,  but  is  prevented ;  the  torsion 
index  being  turned  until  the  twist  on  the  spring  balances 
the  torque.     The  angle  through  which 
the  index   has   had   to   be   turned   is 
proportional  to  the  product  of   C^C^ 
the  currents  in  the  fixed  and  movable 
coils. 

For  use  of  dynamometer  as  ivatt- 
meter,  see  Art.  438. 

396.  Kelvin's  Current  Balances. 
—  Joule,  Mascart,  Lord  Rayleigh,  and 
others  have  measured  currents  by 
balances  in  which  gravity  was  opposed 
to  the  attraction  or  repulsion  of  two 
coils.  Of  such  balances  the  most 
perfect  are  those  of  Lord  Kelvin,  the 
principle  of  which  is  outlined  in  Fig.  204.  There  are  four 
fixed  coils,  ABCD,  between  which  is  suspended,  by  a 
flexible  metal  ligament  of  fine  wires,  at  the  ends  of  a 


Fig.  203. 


Fig.  204. 

light  beam,  a  pair  of  movable  coils,  E  and  F.  The 
current  flows  in  such  directions  through  the  whole  six 
that  the  beam  tends  to  rise  at  F  and  sink  at  E.  The 
beam  carries  a  small  pan  at  the  F  end,  and  a  light  arm, 
not  shown  in  Fig.  204,  but  shown  in  Fig.  205,  along 
which,  as  on  a  steel-yard,  a  sliding  weight  can  be  moved 
to  balance  the  torque  due  to  the  current.  The  current  is 
proportional  to  the  square-root  of  this  torque,  since  the 


394  ELECTRICITY   AND   MAGNETISM      PART  n 


CHAP,  v  CURRENT  BALANCES  395 

force  is  proportional  to  the  product  of  the  current  in  the 
fixed  and  movable  coils  as  in  all  electrodynamometers. 

Lord  Kelvin  has  designed  a  whole  range  *  of  these  instru- 
ments :  — a  centi-ampere  balance  reading  from  O'Ol  to  1  ampere ; 
a  deci-ampere  balance  reading  from  O'l  to  10;  a  deka-ampere 
balance  reading  from  1  to  100 ;  a  hekto-ampere  balance  reading 
from  6  to  000 ;  and  a  kilo-ampere  balance  reading  up  to  2500  am- 
peres. The  centi-ampere  balance  is  shown  in  Fig.  205,  in  which 
the  sliding  weight  is  carried  on  the  base  of  the  pointer  (shown 
white),  and  when  at  the  zero  of  the  scale  just  balances  the  weight 
in  the  V-shaped  pan.  Any  current  passing  through  the  coils  causes 
the  beam  to  tilt  and  the  pointer  is  moved  (by  means  of  a  self- 
releasing  slider  attached  to  cords)  until  it  is  again  horizontal  (as 
shown  by  the  black  pointer  at  either  end) .  With  a  certain  pair  of 
weights  the  fixed  scale  gives  the  current  in  decimal  parts  of  an 
ampere ;  but  by  the  use  of  other  weights  a  wider  range  is  obtained. 

The  "  ampere-standard "  instrument,  and  the  u  volt- 
standard  "  instruments  of  the  Board  of  Trade,  kept  at 
Whitehall  as  legal  standards  for  Great  Britain,  embodying 
the  international  units,  are  current  balances  of  special  con- 
struction, designed  by  Major  Cardew. 

397.  Electromagnetic  Actions  of  Convexion  Currents. 
—  According  to  Faraday  a  stream  of  particles  charged 
with  electricity  acts  magnetically  like  a  true  conduction 
current.  This  was  first  proved  in  1876  by  Rowland,  who 
found  a  charged  disk  rotated  rapidly  to  act  upon  a  mag- 
net as  a  feeble  circular  current  would  do.  Convexion 
currents,  consisting  of  streams  of  electrified  particles,  are 
also  acted  upon  by  magnets.  The  convective  discharges 
iu  vacuum-tubes  (Art.  320)  can  be  drawn  aside  by  a 
magnet,  or  caused  to  rotate  around  a  magnet-pole.  The 
brush  discharge  (Art.  319)  when  taking  place  in  a  strong 
magnetic  field  is  twisted.  The  electric  arc  (Art.  448) 
also  behaves  like  a  flexible  conductor,  and  can  be  attracted 
or  repelled  laterally  by  a  magnet.  Two  stationary  posi- 
tively electrified  particles  repel  one  another,  but  two 

*  For  a  fuller  account  of  these  Current  Balances,  and  of  the  Wattmeters 
on  the  same  principle,  see  Gray's  Absolute  Measurements  in  Electricity 
and  Magnetism,  from  which  Fig.  205  is  taken. 


396  ELECTRICITY   AND   MAGNETISM       PART  n 

parallel  currents  attract  one  another  (Art.  390),  and  if 
electrified  particles  flowing  along  act  like  currents,  there 
should  be  an  (electromagnetic)  attraction  between  two 
electrified  particles  moving  along  side  by  side  through 
space.  According  to  Maxwell's  theory  (Art.  518)  the 
electrostatic  repulsion  will  be  just  equal  to  the  electro- 
magnetic attraction  when  the  particles  move  with  a  velocity 
equal  to  the  velocity  of  light. 

Hall  discovered  in  1879  that  when  a  powerful  magnet 
is  made  to  act  upon  a  current  flowing  along  in  a  strip  of 
very  thin  metal,  the  equipotential  lines  are  no  longer  at 
right  angles  to  the  lines  of  flow  of  the  current  in  the  strip. 
This  action  appears  to  be  connected  with  the  magnetic 
rotation  of  polarized  light  (Art.  526),  the  coefficient  of  this 
transverse  thrust  of  the  magnetic  field  on  the  current 
being  feebly  -f  in  gold,  strongly  +  in  bismuth,  and  —  in 
iron,  and  immensely  strong  negatively  in  tellurium.  It 
was  shown  by  the  author,  and  about  the  same  time  by 
Righi,  that  those  metals  which  manifest  the  Hall  effect 
undergo  a  change  in  their  electric  resistance  when  placed 
in  the  magnetic  field.  The  resistance  of  bismuth  increases 
so  greatly  that  it  affords  a  way  of  measuring  the  strength 
of  magnetic  fields. 

398.  Ampere's  Theory  of  Magnetism.  —  Ampere, 
finding  that  solenoids  (such  as  Fig.  193)  act  precisely  as 
magnets,  conceived  that  all  magnets  are  simply  collections 
of  currents,  or  that  around  every  individual  molecule  of 
a  magnet  an  electric  current  is  ceaselessly  circulating. 
We  know  that  such  currents  could  not  flow  perpetually  if 
there  were  any  resistance  to  them,  and  we  know  that 
there  is  resistance  when  electricity  flows  from  one  mole- 
cule to  another.  As  we  know  nothing  about  the  interior 
of  molecules  themselves,  we  cannot  assert  that  Ampere's 
supposition  is  impossible.  Since  a  whirlpool  of  electricity 
acts  like  a  magnet,  there  seems  indeed  reason  to  think 
that  magnets  may  be  merely  made  up  of  rotating  portions 
of  electrified  matter. 


CHAPTER  VI 

MEASUREMENT    OF   CURRENTS,    ETC. 

LESSON   XXXIII.  —  Ohm's  Laiu  and  its  Consequences 

399.  Law  of  Dr.  Ohm.  —  In  Art.  191  the  law 
discovered  by  Dr.  G.  S.  Ohm  was  stated  in  the  following 
terms :  —  The  strength  of  the  current  varies  directly  as  the 
electromotive-force,  and  inversely  as  the  resistance  of  the 
circuit. 

Using  the  units  adopted  by  practical  electricians,  and 
explained  in  Art.  354,  we  may  now  restate  Ohm's  law  in 
the  following  definite  manner: — The  number  of  amperes 
of  current  flowing  through  a  circuit  is  equal  to  the  number  of 
volts  of  electromotive-force  divided  by  the  number  of  ohms  of 
resistance.  Or, 

amperes  =  volts  -*•  ohms, 
C  =  E/R. 

The  above  is  the  simplest  way  of  stating  the  law,  but 
in  its  application  it  is  not  quite  so  simple.  If  we  apply 
it  to  a  whole  circuit  we  must  consider  both  the  total  E 
and  the  total  R.  For  if  a  number  of  cells  are  used  and 
the  circuit  be  made  up  of  a  number  of  different  parts 
through  all  of  which  the  current  must  flow,  we  have  to 
take  into  account  not  only  the  electromotive-forces  of  the 
cells,  but  their  resistances,  as  well  as  the  resistances  of 
397 


398  ELECTRICITY   AND   MAGNETISM      PART  n 

other  parts  of  the  circuit.  For  example,  the  current  may 
flow  from  the  zinc  plate  of  the  first  cell  through  the  liquid 
to  the  carbon  plate,  then  through  a  connecting  wire  or 
screw  to  the  next  cell,  through  its  liquid,  through  the  con- 
necting screws  and  liquids  of  the  rest  of  the  cells,  then 
through  a  wire  to  a  galvanometer,  then  through  the  coils 
of  the  galvanometer,  then  perhaps  through  an  electrolytic 
cell,  and  finally  through  a  return  wire  to  the  zinc  pole  of 
the  battery.  In  this  case  there  are  a  number  of  separate 
electromotive-forces  all  tending  to  produce  a  flow,  and  a 
number  of  different  resistances,  each  obstructing  the  flow 
and  adding  to  the  total  resistance.  If  in  such  a  case  we 
knew  the  separate  values  of  all  the  different  electromotive- 
forces  and  all  the  different  resistances  that  are  in  series 
we  could  calculate  what  the  current  would  be,  for  it  would 
have  the  value  — 


e't  4. 


rl  _}.   rll  _|_  rIH  -}.   riv  _j_ 

_  Total  electromotive-force 
~~  Total  resistance 

Example.  —  Let  there  be  5  cells  in  series  each  having  e  = 
1-4  volts,  and  each  an  internal  r  =  0-4  ohm ;  and  let  the 
external  part  of  circuit  have  resistance  3  ohms.  Total 
E  =  7  volts ;  total  R  =  5  ohms.  Current  C  will  be  li 
amperes. 

If  any  one  of  the  cells  were  set  wrong  way  round  its 
electromotive-force  would  oppose  that  of  the  other  cells ; 
an  opposing  electromotive-force  must  therefore  be  sub- 
tracted, or  reckoned  as  negative  in  the  algebraic  sum. 
The  "polarization"  (Arts.  175  and  487)  which  occurs 
in  battery  cells  and  in  electrolytic  cells  after  working 
for  some  time  is  an  opposing  electromotive-force,  and 
diminishes  the  total  of  the  electromotive-forces  in  the 
circuit.  So,  also,  the  induced  back  E.M.F.  which  is  set 
up  when  a  current  from  a  battery  drives  an  electric 
motor  (Art.  444)  reduces  the  strength  of  the  working 


CHAP,  vi  OHM'S  LAW 


current;  in  such  case,  if  E  is  the  electromotive-force  of 
the  battery,  e  the  opposing  electromotive-force,  and  R  the 
total  resistance,  we  shall  have 

c  =  E-e 
R 

Example.  —  Suppose  the  battery  to  generate  current  at  25 
volts,  and  the  motor  to  generate  a  back  electromotive- 
force  of  20  volts,  and  the  total  resistance  to  be  2£  ohms, 
there  will  be  a  current  of  2  amperes. 

But  we  may  apply  Ohm's  law  to  a  part  of  a  circuit. 
If  e  represents  the  difference  of  potential  between  two 
ends  of  a  conductor  of  resistance  r,  the  current  C  in  it 
must  be  =  e/r.  Or,  to  put  it  the  other  way  round,  the 
electromotive-force  needed  to  drive  C  amperes  through  a 
resistance  of  r  ohms  will  be  e  =  rC  volts. 

Consider  the  case  of  a  circuit  of  which  the  resistance 
is  made  up  of  two  parts,  an  external  resistance  R  consist- 
ing of  wires,  lamps,  etc.,  and  of  a  smaller  resistance  r  inter- 
nal to  the  battery  or  dynamo  (viz.  the  resistance  of  the 
liquids  in  the  cells,  or  of  the  wire  of  the  armature).  Then 
if  E  is  the  whole  electromotive-force  we  shall  have  as 
current 

c=    E 


or 

or  again  CR  -I-  Cr  =  E. 

This  means  in  words  that  the  total  volts  may  be  considered 
as  being  employed  partly  in  driving  the  current  through 
the  external  resistance  R,  partly  in  driving  the  current 
through  the  internal  resistance  r.  This  latter  part 
of  the  electromotive-force  is  called  the  lost  volts;  the 
remainder  being  the  useful  or  externally  available  volts, 
that  would  be  measurable  by  a  voltmeter  (Art.  220)  set 
across  the  terminals.  If  we  call  the  available  volts  V  we 
may  write  V  =  CR,  whence 


i 

400  ELECTRICITY  AND   MAGNETISM      PART  n 


or  in  words  :  the  volts  as  measured  at  the  terminals  of  a 
cell  or  dynamo  are  less  than  the  whole  E.M.F.  generated 
therein  ;  being  equal  to  the  whole  E.M.F.  less  the  lost 
volts.  The  lost  volts  being  proportional  to  internal 
resistance  it  is  obviously  best  to  keep  all  internal  resist- 
ances as  low  as  possible.  Only  when  the  cell  is  giving  no 
current  are  the  external  volts  V  equal  to  the  whole  E.M.F.  ; 
for  when  C  =  o,  Cr  is  also  =  o. 

Example.  —  A.  dynamo  is  designed  to  generate  its  currents 
with  au  electromotive-force  of  105  volts.  The  internal 
resistance  of  its  armature  is  ^  ohm.  When  it  is  giving 
out  current  of  120  amperes,  the  lost  volts  will  he  120  X  u\j 
=  4  volts.  Consequently  the  volts  available  in  the  exter- 
nal circuit  will  be  only  101. 

Since  C  =  —  ^—  =?  it  follows  also  that  V  =  E     R 


R  +  r     R  R  +  r 

40O.  Resistance.  —  Resistance  is  the  name  given  to 
that  property  of  materials  by  virtue  of  which  they  obstruct 
the  steady  flow  of  electricity  through  them,  and  fritter 
down  into  heat  the  energy  of  the  current.  It  is  found 
that  the  resistance  of  a  metal  wire,  if  kept  at  an  unvary- 
ing temperature,  is  the  same  whether  a  large  current  or 
a  small  current  be  flowing  through  it.  For  example,  if 
a  wire  has  a  resistance  such  that  when  a  difference  of 
potential  of  10  volts  is  applied  to  its  ends  a  current  of  2 
amperes  flows  through  it  (its  resistance  being  5  ohms), 
it  will  be  found  that  if  1  volt  is  applied  the  current  will 
be  0.2  amperes,  the  ratio  between  volts  and  amperes 
being  5  as  before. 

The  unit  of  resistance,  or  ohm,  is  a  standard  chosen  in 
order  that  the  resistances  of  other  conductors  may  be 
expressed  in  definite  numbers.  The  definition  of  it  is 
giveji  in  Art.  354.  It  is  convenient  to  remember  that 
100  yards  of  ordinary  iron  telegraph-wire  has  roughly  a 
resistance  about  1  ohm. 


CHAP,  vi  RESISTANCES  401 

Resistances  in  a  circuit  may  be  of  two  kinds — first, 
the  resistances  of  the  conductors  (metals,  alloys,  liquids) 
themselves;  second,  the  resistances  due  to  imperfect  contact 
at  points.  The  latter  kind  of  resistance  is  affected  by 
pressure,  for  when  the  surfaces  of  two  conductors  are 
brought  into  more  intimate  contact  with  one  another, 
the  current  passes  more  freely  from  one  conductor  to  the 
other.  The  contact-resistance  of  two  copper  conductors 
may  vary  from  infinity  down  to  a  small  fraction  of  an 
ohm,  according  to  the  pressure.  The  variation  of  resist- 
ance at  a  point  of  imperfect  contact  is  utilized  in  telephone 
transmitters  (Art.  512).  The  conduction  of  powdered 
metals  is  remarkable.  A  loose  heap  of  filings  scarcely 
conducts  at  all,  owing  to  the  want  of  cohesion,  or  to  the 
existence  of  films  of  air  or  dust.  But  it  becomes  instantly 
a  good  conductor  if  an  electric  spark  is  allowed  to  occur 
anywhere  within  a  few  yards  of  it  (see  Art.  521).  The 
resisting  films  of  air  are  broken  down  by  minute  internal 
discharges  in  the  mass.  A  very  slight  agitation  by  tap- 
ping at  once  makes  the  powder  non-conductive. 

For  the  purpose  of  regulating  the  flow  of  currents, 
and    for    electrical    measurements    (Art.    411),   variable 
resistances  are  employed.  Resist- 
ance coils  (Art.  414)  are  sets  of 
coils  made  each  of   a  definite 
value  in  ohms,  of  which  one  or 
more  can   be   inserted  in  the 
circuit  at  will.  Rheostats  consist 
of  easily-adjustable  resistances,  Fig.  206. 

the   length  of  wire  in  circuit 

being  varied  by  turning  a  handle.  In  some  cases  the 
rheostat  wire  is  wound  off  and  on  to  a  roller.  In 
others  a  handle  (Fig.  206)  moving  over  a  number  of 
metal  studs  varies  the  amount  of  resistance-wire  through 
which  the  current  must  flow.  Carbon  rheostats  consist  of 
a  number  of  little  plates  of  hard  carbon,  about  3  inches 
square,  arranged  in  a  pile,  with  a  screw  to  reduce  their 

2D 


402  ELECTRICITY   AND   MAGNETISM      PART  11 

resistance  by  squeezing  them  together  into  better  con- 
tact. 

401.  Laws  of  Resistance.  —  The  following   are  the 
laws  of  the  resistance  of  conductors:  — 

(i .)  The  resistance  of  a  conducting  wire  is  proportional  to 
its  length.  If  the  resistance  of  a  mile  of  iron 
telegraph  wire  be  17  ohms,  that  of  50  miles  will 
be  50  x  17  =  850  ohms. 

(ii.)  The  resistance  of  a  conducting  wire  is  inversely  pro- 
portional to  the  area  of  its  cross-section,  and  therefore 
in  the  usual  round  wires  is  inversely  proportional 
to  the  square  of  its  diameter.  Ordinary  telegraph 
wire  is  about  |-  of  an  inch  thick;  a  wire  twice 
as  thick  would  conduct  four  times  as  well, 
having  four  times  the  area  of  cross  -  section  • 
hence  an  equal  length  of  it  would  have  only  \ 
the  resistance. 

(iii.)  The  resistance  of  a  conducting  wire  of  given  length 
and  thickness  depends  upon  the  material  of  which 
it  is  made — that  is  to  say,  upon  the  specific 
resistance  of  the  material. 

If  the  length  of  a  wire  be  I  centimetres,  and  its  area 
of  section  A  square  centimetres,  arid  the  specific  resistance 
of  the  material  be  p,  then  its  resistance  R  will  be 

R  =  lp/ A. 

Example.  —  Find  the  resistance  of  a  platinoid  wire  of  sec- 
tion 0*004  sq.  cm.,  and  200  cm.  long;  P  =  32'5  X  10-6. 
K  =  1-025  ohms. 

402.  Conductance   and   Resistance. —  The  term  con- 
ductance is  used  as  the  inverse  of  resistance ;  a  conductor 
whose  resistance  is  r  ohms  is  said  to  have  a  conductance 
of   l/r  "mhos."      When   a  number  of  conductors  are  in 
parallel  with  one  another  their  united  conductance  is  the 
sum  of  their  separate  conductances. 

The  conductance  of  a  prism  of  which  the  length  is 


RESISTIVITY  403 


1  cm.  and  its  area  of  section  is  1  sq.  cm.,  is  called  its 
conductivity  or  specific  conductance. 

The  resistance  of  a  prism  of  length  1  cm.  and  section 
1  sq.  cm.  is  sometimes  called  its  resistivity  or  specific 
resistance. 

403.  Specific  Resistance.  —  The  specific  resistance  of 
a  substance  is  most  conveniently  stated  as  the  resistance 
(in  rnillionths  of  an  ohm)  of  a  centimetre  cube  of  the 
substance.      The  Table  on  p.  404  also  gives  the  relative 
conductance  when  that  of  copper  is  taken  as  100 :  — 

Aluminium  is  a  better  conductor  than  silver,  weight 
for  weight. 

It  is  found  that  those  substances  that  possess  a  high 
conducting  power  for  heat  are  also  the  best  conductors 
of  electricity,  but  the  ratio  of  these  conductivities  is 
not  constant ;  it  varies  as  the  absolute  temperature. 

Liquids  fall  under  three  heads  :  (1)  molten  metals  and 
alloys,  which  conduct  simply  as  metals ;  (2)  fused  salts 
and  solutions  of  salts  and  acids,  which  conduct  only  by 
electrolysis  (Art.  487)  ;  (3)  insulators,  such  as  the  oils,  tur- 
pentine, etc.,  and  bromine.  Liquid  electrolytes  are  worse 
conductors  than  metals ;  gases,  including  steam,  are  per- 
fect non-conductors,  except  when  so  rarefied  as  to  admit 
of  discharge  by  convexion  through  them  (Art.  320). 

404.  Effects   of  Heat  on   Resistance.  —  Changes  of 
temperature    affect    temporarily   the   conducting   power 
of   metals.       Nearly  all   the  pure  metals  increase  their 
resistance  about  04  per  cent  for  a  rise  of  1°  C.  in  tem- 
perature, or    about    40    per    cent  when   warmed   100°. 
When  cooled  in  liquid  oxygen  the  resistance  was  found 
by  Wroblewski  to  fall  greatly.     A  copper  wire  which  at 
0°  had  a  resistance  of    17-5  ohms   fell  to  1-65  ohms  at 
—  201°  C.     Dewar  and  Fleming  find  all  pure  metals  to 
lower  their  resistance  as  though  at  —  274°  C.  (absolute 
zero   of   temperature)  they  would  become   perfect   con- 
ductors.    The  resistance  of  carbon,  on  the  other  hand, 
diminishes  on  heating.      The  filament  of  a  glow-lamp, 


404 


ELECTRICITY  AND   MAGNETISM      PART  n 


TABLE  OF  SPECIFIC    KESISTANCE. 


Substance. 

Specific 
Resistance 
(microhms  of 
1  cm.  cube). 

Resistance 
(ohms)  of 
metre  length 
1  sq.  mm. 
Section. 

Relative 
Conductance. 

Metals  at  0°  C. 

Copper  (annealed) 
"       (hard) 

1-570 
1-603 

•0157 
•0160 

100 
98-1 

Silver  (annealed)  . 

1-492 

•0149 

105 

"     (hard)  . 

1-620 

•0162 

98 

Gold       .... 

2-077 

•0208 

76 

Aluminium   (annealed) 

2-889 

.     -0289 

54 

Platinum 

8-982 

•0898 

17 

Iron  (pure)    . 

9-G38 

•0964 

16 

Iron  (telegraph  wire)    . 

15 

•15 

10 

Lead      .... 

19-63 

•1963 

8-3 

Mercury 

94-34 

•9434 

1-6 

Selenium 
Carbon  (graphite) 

6  x  10*0 
2400  to  42000 

40>000>  OOO'OOO 

"       (arc  light) 

about  4000 

UB^O 

Alloys. 

German-silver 

20'76 

•2076 

7-6 

(Cu  60,  Zn  26,  Ni  14) 

Platinum-silver     . 

2-4 

•024 

6-5 

(Pt  67,  Ag  33) 

Platinoid 

32-5 

•325 

4-8 

(Cu  59,  Zn  25-5,  Ni 
14,  W  55) 

Manganin 

47-5 

•475 

3-3 

(Cu  84,  Ni  12,  Mn  3'5) 

Liquids  at  18°  C. 

Pure  water    . 

26-5  x  108 

less  than  ono 

Dilute  II,SO4,  5% 
"      II2S64,80%        . 

486  x  10* 
137  x  Id* 

millionth  part 

"      H2S04,  80% 

91SX10* 

"      Zn8O4,  24% 

214x108 

"      1IN03,  81)  %        . 

129  x  104 

Insulators. 

Glass  at  20°  C. 

91  x  1018 

Glass  at  200°  C.     . 

22-7  x  H)i2 

less  than  one 

Guttapercha  24°  C. 

4-5  x  Hi™ 

billionth 

CHAP,  vi  INSULATORS  405 

which  when  cold  was  230  ohms,  was  only  150  when  white 
hot.  German-silver  and  other  alloys  do  not  show  so 
much  change,  hence  they  are  used  in  making  standard 
resistance  coils.  The  temperature-coefficient  of  German- 
silver  is  only  0-00044  for  1°  C.,  or  TV  that  of  the  pure 
metals.  Platinoid  and  platinum-silver  have  about  0-00011 
for  their  coefficient.  Weston  has  found  alloys  of  man- 
ganese, copper,  and  nickel,  which  have  a  small  negative 
coefficient.  Those  liquids  which  only  conduct  by  being 
electrolyzed  (Art.  234)  conduct  better  as  the  tempera- 
ture rises.  The  effect  of  light  in  varying  the  resist- 
ance of  selenium  is  stated  in  Art.  529.  The  property 
of  changing  resistance  with  temperature  is  now  used 
for  measuring  furnace  temperatures  in  Callendar's 
platinum  pyrometer.  The  bolometer  used  by  Langiey 
in  researches  011  radiant  heat  depends  on  the  same 
property. 

405.  Insulators.  —  The  name  insulators  is  given  to 
materials  which  have  such  high  resistances  that  they  can 
be  used  as  non-conductors.  They  differ  much  in  their 
mechanical  qualities  as  well  as  in  their  insulation-resist- 
ance. They  may  be  classed  under  several  heads :  (1) 
Vitreous,  including  glass  of  all  kinds  and  slags ;  (2)  Stony, 
including  slate,  marble,  stoneware,  steatite,  porcelain, 
mica,  asbestos ;  (3)  Resinous,  including  shellac,  resin,  bees- 
wax, pitch,  various  gums,  bitumen,  ozokerit ;  (4)  Elastic, 
including  india-rubber,  guttapercha,  ebonite ;  (5)  Oily, 
including  various  oils  arid  fats  of  animal  and  vegetable 
origin,  as  well  as  solid  paraffin  and  petroleum  oil;  (G) 
Cellulose,  including  dry  wood  and  paper,  and  preparations 
of  paper,  such  as  "fibre"  and  celluloid.  All  these 
materials  decrease  their  resistance  enormously  as  the 
temperature  rises,  and  in  general  become  fairly  good 
conductors  as  soon  as  any  chemical  change  begins ;  some 
of  them  (as  glass)  conduct  as  electrolytes  so  soon  as 
they  soften. 

The  name  insulators  is  also  used  for  the  insulating 


406 


ELECTRICITY   AND   MAGNETISM      PART  n 


supports  of  stoneware,  porcelain,  or  glass  on  which  tele- 
graph wires  are  carried  (Art.  497). 

406.  Typical  Circuit.  —  Let  us  consider  the  typical 
case  of  the  circuit  shown  in  Fig.  207,  in  which  a  battery, 
ZC,  is  joined  up  in  circuit  with  a  galvanometer  by  means 
of  wires  whose  resistance  is  R.  The  total  electromotive- 
force  of  the  battery  we  will  call  E,  and  the  total  internal 
resistance  of  the  liquids  in  the  cells  r.  The  resistance  of 
the  galvanometer  coils  may  be  called  G.  Then,  by  Ohm's 
law:  — 


r\  


E 


JSi_ 


Fig.  20T. 


R  +  r  +  G 

The  internal  resistance  r  of  the  liquids  of  the  battery 
bears  an  important  relation  to  the  external  resistance  of 

the  circuit  (including  E, 
and  G),  for  on  this  relation 
depends  the  best  way  of 
arranging  the  battery  cells. 
Suppose,  for  example,  that 
we  have  a  battery  of  50 
small  Daniell's  cells  at  our 
disposal,  of  which  we  may 
reckon  the  electromotive- 
force  as  one  volt  (or,  more 
accurately,  1-07  volt)  each,  and  each  having  an  internal 
resistance  of  two  ohms.  If  we  have  to  use  these  cells  on 
a  circuit  where  there  is  already  of  necessity  a  high  resist- 
ance, we  should  couple  them  up  "  in  series  "  rather  than 
in  parallel.  For,  supposing  we  have  to  send  our  current 
through  a  line  of  telegraph  100  miles  long,  the  external 
resistance  R  will  be  (reckoning  13  ohms  to  the  mile  of 
wire)  at  least  1300  ohms.  Through  this  resistance  a 
single  such  cell  would  give  a  current  of  less  than  one  milli- 
ampere,  for  here  E  =  1,  R  =  1300,  r  —  2,  and  therefore 

F  1  1 

C  = = = of  an  ampere,  a  current  far 

R  +  r      1300  +  2     1302 
too  weak  to  work  a  telegraph  instrument. 


CHAP,  vi  CIRCUIT   CALCULATIONS  407 

With  fifty  such  cells  in  series  we  should  have  E  =  50, 
r  =  100,  and  then 

C  = — =  — —  =  —  of  an  ampere,  or  over  35  milli- 

1300  +  100      1400     28 

amperes.  In  telegraph  work,  where  the  instruments 
require  a  current  of  5  to  10  milli-amperes  to  work  them, 
it  is  usual  to  reckon  an  additional  Daniell's  cell  for  every 
5  miles  of  line,  each  instrument  in  the  circuit  being- 
counted  as  having  as  great  a  resistance  as  10  miles  of 
wire. 

If,  however,  the  resistance  of  the  external  circuit  be 
small,  such  arrangements  must  be  made  as  will  keep  the 
total  internal  resistance  of  the  battery  small.  Suppose, 
for  example,  we  wish  merely  to  heat  a  small  piece  of 
platinum  wire  to  redness,  and  use  stout  copper  wires  to 
connect  it  with  the  battery.  Here  the  external  resist- 
ance may  possibly  not  be  as  much  as  1  ohm.  In  that 
case  a  single  cell  would  give  a  current  of  |  of  an  ampere 
(or  333  milli-amperes)  through  the  wire,  for  here  E  =  1, 
11  =  1,  and  r  =  2.  But  10  cells  would  only  give  half  as 
much  again,  or  476  milli-amperes,  and  fifty  cells  only 
495  milli-amperes,  and  with  an  infinite  number  of  such 
cells  in  series  the  current  could  not  possibly  be  more 
than  500  milli-amperes,  because  every  cell,  though  it  adds 
1  to  E,  adds  2  to  R.  It  is  clear  then  that  though  link- 
ing many  cells  in  series  is  of  advantage  where  there  is  the 
resistance  of  along  line  of  wire  to  be  overcome,  yet  where 
the  external  resistance  is  small  the  practical  advantage  of 
adding  cells  in  series  soon  reaches  a  limit. 

But  suppose  in  this  second  case,  where  the  external 
resistance  of  the  circuit  is  small,  we  reduce  also  the 
internal  resistance  of  our  battery  by  linking  cells  to- 
gether in  parallel,  joining  several  zincs  of  several  cells 
together,  and  joining  also  their  copper  poles  together 
(as  suggested  in  Art.  192),  a  different  and  better  result 
is  attained.  Suppose  we  thus  join  up  four  cells.  Their 
electromotive-force  will  be  no  more,  it  is  true,  than  that 


408  ELECTRICITY  AND    MAGNETISM      PART  n 


of  one  cell,  but  their  resistance  will  be  but  !  of  one  such 
cell,  or  ^  an  ohm.  These  four  cells  would  give  a  current 
of  666  milli-amperes  through  an  external  resistance  of  1 
ohm,  for  if  E  =  1,  R  =  1,  and  the  internal  resistance 
be  I  of  r.  or  =  A,  then 

F 

C  =  —  —  —  |  of  an  ampere,  or  666  milli-amperes. 

If  we  arrange  the  cells  of  a  battery  in  n  files  of  m 
cells  in  series  in  each  file  (there  being  m  x  n  similar  cells 
altogether),  the  electromotive-force  of  each  file  will  be 
m  times  the  electromotive-force  E  of  each  cell,  or  mE  ; 
and  the  resistance  of  each  file  will  be  m  times  the  resist- 
ance r  of  each  cell,  or  mr.  But  there  being  n  files  in 

parallel  the  whole   internal  resistance   will   be   only   - 

of  the  resistance  of  any  one  file,  or  will  be  —r,  hence, 

n 
by  Ohm's  law,  such  a  battery  would  give  as  its  current 

C=     mE    • 


407.  Best  Groupings  of  Cells.  —  If  the  question 
arises  as  to  the  best  way  of  grouping  a  given  number  of 
cells,  it  must  be  replied  that  there  are  several  best  ways. 

(1)  Grouping  for  best  Economy.  —  So  group  the  cells 
that  their  united  internal  resistance  shall  be  very  small 
compared  with   the  external  resistance.      In   this  case 
the  materials  of  the  battery  will  be  consumed  slowly,  and 
the  current  will  not  be  drawn  off  at  its  greatest  possible 
strength  ;  but  there  will  be  a  minimum  waste  of  energy 
(Art.  435). 

(2)  Grouping  for  greatest  Current.  —  It  can  be  shown 
mathematically  that,  for  a  given  battery  of  cells,  the  way 
of  grouping  them  that  will  give  the  largest  steady  current 
when  they  are  required  to  work  through  a  given  external 
resistance  R,   is  so  to  choose  m  and  n  that  the  internal 

resistance  (  —  r\  shall  equal  the  external  resistance.     The 


CHAP,  vi  GROUPING  OF  CELLS  409 

student  should  verify  this  rule  by  taking  examples  and 
working  them  out  for  different  groupings  of  the  cells. 
Although  this  arrangement  gives  the  strongest  current  it  is 
not  the  most  economical;  for  if  the  internal  and  external 
resistances  be  equal  to  one  another,  the  useful  work  in 
the  outer  circuit  and  the  useless  work  done  in  heating  the 
cells  will  be  equal  also,  half  the  energy  being  wasted. 

(3)  Grouping  for  quickest  Action.  —  If  there  are  electro- 
magnets, or  other  objects  possessing  self-induction  (Art. 
458)  in  the  circuit,  which  would  tend  to  prevent  the 
current  rising  quickly  to  its  proper  value,  the  best  group- 
ing to  cause  the  current  to  rise  as  quickly  as  possible  is 
one  that  will  make  the  internal  resistance  higher  than  the 
external,  namely,  put  all  the  cells  in  series  (see  Art.  460). 

408.  Long  and  Short  Coil  Instruments.  —  The  stu- 
dent will  also  now  have  no  difficulty  in  perceiving  why 
a  "  long-coil "  galvanometer,  or  a  "  long-coil  "  electromag- 
net, or  instrument  of  any  kind  in  which  the  conductor 
is   a  long  thin  wire   of  high   resistance,  must  not  be 
employed  on  circuits  where  both  R  and  r  are  already 
small.     He  will  also  understand  why,  on  circuits  of  great 
length,  or  where  there  is  of  necessity  a  high  resistance  and 
a  battery  of  great  electromotive-force  is  employed,  "  short- 
coil  "  instruments  are  of  little  service,  for  though  they 
add  little  to  the  resistances,  their  few  turns  of  wire  are  not 
enough  to  produce  the  required  action  with  the  small  cur- 
rents that  circulate  in  high-resistance  circuits.     He  will 
understand,  too,  why  "  long-coil "  instruments  are  here 
appropriate  as  multiplying  the  effects  of  the  currents  by 
their  many  turns,  their  resistance,  though  perhaps  large, 
not  being  a  serious  addition  to  the  existing  resistances  of 
the  circuit.     The  main  point  to  grasp  is  that  it  is  the 
nature  of  the  line,  whether  of  high  resistance  or  low,  which 
determines  not  only  the  grouping  of  the  battery,  but  also 
what  kind  of  winding  is  appropriate  in  the  instruments. 

409.  Divided   Circuits.  —  If  a  circuit  divides,  as  in 
Fig.  208,  into  two  branches  at  A,  uniting  together  again 


410 


ELECTRICITY   AND   MAGNETISM      PART  n 


at  B,  the  current  will  also  be  divided,  part  flowing  through 
one  branch,  part  through  the  other.  Any  branch  which 
serves  as  a  by-pass  to  another  branch  is  termed  a  shunt. 
The  relative  strengths  of  current  in  the  two  branches  will  be 

proportional  to  their  con- 
ductances, i.e.  inversely 
proportional  to  their  resist- 
ances.* Thus,  if  r  be  a 
wire  of  2  ohms  resistance 
and  r'  3  ohms,  then 
current  in  r:  current  in 
r'=r':r  =  3:2, 
or,  f  of  the  whole  cur- 
rent will  flow  through  r,  and  f  of  the  whole  current 
through  r'. 

The  joint  resistance  of  the  divided  circuit  between  A 
and  B  will  be  less  than  the  resistance  of  either  branch 
singly,  because  the  current  has  now  two  paths.  In  fact, 
the  joint  conductance  will  be  the  sum  of  the  two  separate 
conductances.  And  if  we  call  the  joint  resistance  R,  it 
follows  that 

1      1      1       r'  +  r 
R      r      r'         rr'    ' 

whence  R  — ,  or,  in  words,   the  joint  re- 

r'+r 

sistance  of  a  divided  conductor  is  equal  to  the  product  of  the 
two  separate  resistances  divided  by  their  sum.  This  is  some- 
times called  the  law  of  shunts,  because  each  of  the  branches 
may  be  regarded  as  a  shunt  to  the  other.  A  simple  con- 
struction for  finding  the  value  graphically  is  given  in  Fig. 
209.  Let  lines  representing  the  two  resistances  r  and  r' 
be  erected  at  the  ends  of  any  base  line,  and  the  diagonals 

*  There  is  a  popular  fallacy  that  an  electric  current  "  always  takes  the 
line  of  least  resistance."  It  never  does,  though  part  of  the  current  may 
flow  that  way.  It  divides  between  the  various  paths  in  proportion  to  their 
easiness.  It  is  only  spark  discharges  which  pierce  a  non-conductor  that 
can  be  said  to  take  the  line  of  least  resistance. 


CHAP,  vi       RESISTANCES   IN   PARALLEL 


411 


drawn  as  shown.     The  perpendicular  at  the  point  of  their 
intersection  will  be  the  joint  resistance  R. 

In  case  there  are  three  or  more  branches  all  in  parallel, 
as  in  Fig.  210,  the  rule  may  be  generalized  as  follows :  — 


Fig.  209. 


Fig.  '210. 


The  joint  resistance  of  any  number  of  conductors  in  parallel 
is  the  reciprocal  of  the  sum  of  the  reciprocals  of  the  separate 
resistances. 

Kirchhoff  has  given  the  following  important  laws,  both 
of  them  deducible  from  Ohm's  law. 

(i.)  In  any  branching  network  of  wires  the  algebraic  sum 
of  the  currents  in  all  the  ivires  that  meet  in  any 
point  is  zero. 

(ii.)  When  there  are  several  electromotive-forces  acting  at 
different  points  of  a  circuit,  the  total  electromotive- 
force  round  the  circuit  is  equal  to  the  sum  of  the 
resistances  of  its  separate  parts  multiplied  each  into 
(lie  strength  of  the  current  that  flows  through  it. 

410.  Current  Sheets.  —  When  a  current  enters  a  solid 
conductor  it  no  longer  flows  in  one  line  but  spreads 
out  and  flows  through  the  mass  of  the  conductor.  When 
a  current  is  led  into  a  thin  plate  of  conducting  matter  it 
spreads  out  into  a  current  sheet  and  flows  through  the  plate 
by  stream-lines  in  directions  that  depend  upon  the  form  of 
the  plate  and  the  position  of  the  pole  by  which  it  returns 
to  the  battery.  Thus,  if  wires  from  the  two  poles  of  a 
battery  are  brought  into  contact  with  two  neighbouring 


412  ELECTRICITY   AND   MAGNETISM      PART  11 

points  A  and  B  in  the  middle  of  a  very  large  flat  sheet 
of  tinfoil,  the  current  flows  through  the  foil  not  in  one 
straight  line  from  A  to  B,  but  in  stream-lines,  which  start 
out  in  all  directions  from  A,  and  curl  round  to  meet  in 
B,  in  curves  very  like  those  of  the  "lines  of  force"  that 
run  from  the  N  pole  to  the  S  pole  of  a  magnet  (Fig.  67). 
When  the  earth  is  used  as  a  return  wire  to  conduct  the 
telegraph  currents  (Fig.  274),  a  similar  spreading  of  the 
currents  into  current  sheets  occurs. 


LESSON  XXXIV.  —  Electrical  Measurements 

411.  Measurement  of  Resistance.  —  The  practical  elec- 
trician has  to  measure  electrical  resistances,  electromotive- 
forces,  and  the  capacities  of  condensers.  Each  of  these 
several  quantities  is  measured  by  comparison  with  ascer- 
tained standards,  the  particular  methods  of  comparison 
varying,  however,  to  meet  the  circumstances  of  the  case. 
Only  a  few  simple  cases  can  be  here  explained. 

Ohm's  law  shows  us  that  the  strength  of  a  current  due 
to  an  electromotive-force  falls  off  in  proportion  as  the 
resistance  in  the  circuit  increases. 

(a)  Method  of  Substitution.  —  It  is  therefore  possible  to 
compare  two  resistances  with  one  another  by  finding  out 
in  what  proportion  each  of  them  will  cause  the  current  of 
a  constant  battery  to  fall  off.  Thus,  suppose  in  Fig.  207 
we  have  a  standard  battery  of  a  few  Daniell's  cells, 
joined  up  in  circuit  with  a  wire  of  an  unknown  resistance 
K,  and  with  a  galvanometer,  we  shall  obtain  a  current  of 
a  certain  strength,  as  indicated  by  the  galvanometer  needle 
experiencing  a  certain  deflexion.  If  we  remove  the  wire 
It,  and  substitute  in  its  place  in  the  circuit  wires  whose 
resistances  we  know,  we  may,  by  trying,  find  one  which, 
when  interposed  in  the  path  of  the  current,  gives  the  same 
deflexion  on  the  galvanometer.  This  wire  and  the  one 
we  called  R  offer  equal  resistance  to  the  current.  This 


CHAP,  vi     MEASUREMENT  OF   RESISTANCE  413 

method  of  substitution  of  equivalent  resistances  was  further 
developed  by  Wheatstone,  Jacobi,  and  others,  when  they 
proposed  to  employ  as  a  standard  resistance  a  long  thin 
wire  coiled  upon  a  wooden  cylinder,  so  that  any  desired 
length  of  the  standard  wire  might  be  thrown  into  the 
circuit  by  unwinding  the  proper  number  of  turns  of  wire 
off  the  cylinder,  or  by  making  contact  at  some  point  at 
any  desired  distance  from  the  end  of  the  wire.  This  form 
of  rheostat  was  found,  however,  to  be  less  accurate  than 
the  resistance  coils  described  below. 

(b)  Method  of  Proportional  Deflexion.  —  The  method 
explained  above  can  be  used  with  any  galvanometer  of 
sufficient  sensitiveness,  but  if  a  tangent  galvanometer  is 
available  the  process  may  be  shortened  by  calculation. 
Suppose  the  galvanometer  and  an  unknown  resistance  R 
to  be  included  in  the  circuit,  as  in  Fig.  207,  and  that  the 
current  is  strong  enough  to  produce  a  deflexion  8 :   Now 
substitute  for  R  any  known  resistance  R',  which  will  alter 
the  deflexion  to  8';  then  (provided  the  other  resistances  of 
the  circuit  be  negligibly  small)  it  is  clear  that  since  the 
strengths  of  the  currents  are  proportional  to  tan  8  and 
tan  8'  respectively,  the  resistance  R  can  be  calculated  by 
the  inverse  proportion. 

tan  8  :  tan  8'  =  R' :  R. 

(c)  Method  of  Differential  Galvanometer.  —  With  a  dif- 
ferential galvanometer  (Art.  217),  and  a  set  of  standard 
resistance  coils,  it  is  easy  to  measure  the  resistance  of  a 
conductor.     Let  the  circuit  divide  into  two  branches,  as 
in  Fig.  211,  so  that  part  of  the  current  flows  through  the 
unknown  resistance  and  round  one  set  of  coils  of  the 
galvanometer,  the  other  part  of  the  current  being  made  to 
flow  through  the  known  resistances  and  then  round  the 
other  set  of  coils  in  the  opposing  direction.     When  we 
have  succeeded  in  matching  the  unknown  resistance  by 
one  equal  to  it  from  amongst  the  known  resistances,  the 
currents  in  the  two  branches  will  be  equal,  and  the  needle 


414  ELECTRICITY   AND   MAGNETISM       TAUT  n 

of  the  differential  galvanometer  will  show  no  deflexion. 
This  null  method  is  very  reliable. 

(d)  Bridge   Method.  —  The   best   of  all  the  ways  of 
measuring   resistances   is,  however,  with  the   important 
instrument  known    as   Wheatstone's   Bridge,   described 
below  in  Art.  413. 

(e)  Condenser  Methods.  —  To  measure  very  high  resist- 
ances the  plan  may  be  adopted  of  charging  a  condenser 

from  a  standard  battery  for  a  definite 
Diff}      time  through  the  resistance,  and  then 
ascertaining  the  accumulated  charge 
by  discharging  it  through  a  ballistic 
galvanometer  (Art.  218).     Or  in  an- 
other method  the  condenser  is  allowed 
to  discharge  itself  slowly  through  the 
high  resistance,  and  the  time  taken 
by  the  potential  to  fall  through  any 
given  fraction  of  its  original  value  is 
observed.     This  time  is  proportional 
to  the  resistance,  to  the  capacity,  and  to  the  logarithm  of 
the  given  fraction. 

412.  Fall  of  Potential  along  a  Wire. —  To  under- 
stand the  principle  of  Wheatstone's  Bridge  we  must  ex- 
plain a  preliminary  point.  If  the  electric  potential  of 
different  points  of  a  circuit  be  examined  by  means  of  an 
electrometer,  as  explained  in  Art.  289,  it  is  found  to 
decrease  all  the  way  round  the  circuit  from  the  -f  pole  of 
the  battery,  where  it  is  highest,  down  to  the  —pole,  where 
it  is  lowest.  If  the  circuit  consist  of  one  wire  of  uniform 
tli ick ness,  which  offers,  consequently,  a  uniform  resistance 
to  the  current,  it  is  found  that  the  potential  falls  uni- 
formly ;  if,  however,  part  of  the  circuit  resists  more  than 
another,  it  is  found  that  the  potential  falls  most  rapidly 
along  the  conductor  of  greatest  resistance.  If  with  a  suit- 
able voltmeter  we  explore  the  fall  of  potential  between  two 
points  a  and  &  of  a  circuit  (Fig.  212),  we  shall  find  in  every 
case  the  fall  of  potential  proportional  to  the  resistance 


FALL   OF   POTENTIAL  415 


between  those  two  points.  For  V  —  CR,  and  therefore,  for 
the  same  C,  the  V  across  any  part  is  proportional  to  the 
R  of  that  part.  We  know,  for  example,  that  when  we 
have  gone  round  the  circuit  to  a  point  where  the  potential 
has  fallen  through  half  its  value,  the  current  has  at  that 
point  gone  through  half  the 
resistances.  The  best  way  to 
measure  a  very  large  current 
is  to  measure  (with  sensitive 
voltmeter  arrangement  of  gal- 
vanometer) the  drop  of  poten- 
tial it  produces  when  sent  212. 
through  a  known  very  low- 
resistance  such  as  a  strip  of  platinoid  having  exactly 
TWO  ohm  resistance  between  two  measured  points. 
To  measure  a  very  small  resistance,  it  should  be  put  in 
series  with  another  known  very  small  resistance,  and 
the  drops  of  potential  when  the  same  current  flows 
through  both  are  compared :  the  resistance  of  each  being 
as  the  drop  in  potential  between  its  ends. 

413.  Wheatstone's  Bridge.  —  This  instrument,  in- 
vented by  Christie,  and  applied  by  Wheatstone  to  meas- 
ure resistances,  consists  of  a  system  of  conductors  shown 
in  diagram  in  Fig.  '213.  This  circuit  of  a  battery  is  made 
to  branch  at  P  into  two  parts,  which  reunite  at  Q,  so 
that  part  of  the  current  flows  through  the  point  M,  the 
other  part  through  the  point  N.  The  four  conductors 
D,  C,  B,  A,  are  spoken  of  as  the  "  arms  "  of  the  "  balance  '• 
or  "bridge  "  ;  it  is  by  the  proportion  subsisting  between 
their  resistances  that  the  resistance  of  one  of  them  can  be 
calculated  when  the  resistances  of  the  other  three  are 
known.  When  the  current  which  starts  from  C  at  the 
battery  arrives  at  P,  the  potential  will  have  fallen  to  a 
certain  value.  The  potential  of  the  current  in  the  upper 
branch  again  falls  to  M,  and  continues  to  fall  to  Q.  The 
potential  of  the  lower  branch  falls  to  N,  and  again  falls 
till  it  reaches  the  value  at  Q.  Now  if  N  be  the  same 


416 


ELECTRICITY  AND   MAGNETISM      PART  n 


proportionate  distance  along  the  resistances  between  P 
and  Q,  as  M  is  along  the  resistances  of  the  upper  line 
between  P  and  Q,  the  potential  will  have  fallen  at  N  to 
the  same  value  as  it  has  fallen  to  at  M ;  or,  in  other 
words,  if  the  ratio  of  the  resistance  C  to  the  resistance  D 


Fig.  213. 

be  equal  to  the  ratio  between  the  resistance  A  and  the 
resistance  B,  then  M  and  N  will  be  at  equal  potentials. 
To  find  out  whether  they  are  at  equal  potentials  a  sensi- 
tive galvanometer  is  placed  in  a  branch  wire  between  M 
and  N ;  it  will  show  no  deflexion  when  M  and  N  are  at 
equal  potentials ;  or  when  the  four  resistances  of  the  arms 
"  balance  "  one  another  by  being  in  proportion,  thus :  — 

A  :  C  :  :  B  :  D. 

If,  then,  we  know  what  A,  B,  and  C  are,  we  can  calculate 
D,  which  will  be 

B  x  C 


Example.—  Thus  if  A  and  C  are  (as  in  Fig.  216)  10  ohms 
and  100  ohms  respectively,  and  B  be  15  ohms,  D  will  be 
15  X  100  -T-  10  =  150  ohms. 


RESISTANCE   COILS 


417 


414.  Resistance  Coils. —Wires  of  standard  resist- 
ance are  now  sold  by  instrument-makers  under  the 
name  of  Resistance  Coils.  They  consist  of  coils  of  some 
alloy,  German-silver,  platinum-silver,  or  platinoid  (see 
Art.  404),  wound  with 
great  care,  and  adjusted 
to  such  a  length,  as  to 
have  resistances  of  a  de- 
finite number  of  ohms. 
In  order  to  avoid  self- 
induction,  and  the  con- 
sequent sparks  (see  Art. 
458)  at  the  opening  or 
closing  of  the  circuit, 


Fig.  214. 


they  are  wound  in  the  peculiar  non-inductive  manner 
indicated  in  Fig.  214,  each  wire  (covered  with  silk  or 
paraffined-cotton)  being  doubled  on  itself  before  being 
coiled  up.  Each  end  of  a  coil  is  soldered  to  a  solid  brass 


Fig.  215. 

piece,  as  coil  1  to  A  and  B,  coil  2  to  B  and  C ;  the  brass 
pieces  being  themselves  fixed  to  a  block  of  ebonite  (form- 
ing the  top  of  the  "resistance-box"),  with  sufficient  room 
between  them  to  admit  of  the  insertion  of  stout  well- 
fitting  plugs  of  brass.  Fig.  215  shows  a  complete  resist- 
ance-box, as  fitted  up  for  electrical  testing,  with  the  plugs 
in  their  places.  So  long  as  the  plugs  remain  in,  the 
2  K 


418 


ELECTRICITY   AND   MAGNETISM      PART  n 


current  flows  through  the  solid  brass  pieces  and  plugs 
without  encountering  any  serious  resistance;  but  when 
any  plug  is  removed,  the  current  can  only  pass  from  the 
one  brass  piece  to  the  other  by  traversing  the  coil  thus 
thrown  into  circuit.  The  series  of  coils  chosen  is  usually 
of  the  following  numbers  of  ohms'  resistance  —  1,  2, 
2,  5;  10,  20,  20,  50;  100,  200,  200,  500;  ...  up  to 
10,000  ohms.  By  pulling  out  one  plug  any  one  of  these 
can  be  thrown  into  the  circuit,  and  any  desired  whole 


Fig.  '216. 

number,  up  to  20,000,  can  be  made  up  by  pulling  out 
more  plugs ;  thus  a  resistance  of  2(33  ohms  will  be  made 
up  as  200  +  50+10  +  2+1  by  unplugging  those  five 
coils. 

It  is  usual  to  construct  Wheatstone's  bridges  with  some 
balancing  resistance  coils  in  the  arms  A  and  C,  as  well  as 
with  a  complete  set  in  the  arm  B.  The  advantage  of  this 
arrangement  is  that  by  adjusting  A  and  C  we  determine 
the  proportionality  between  B  and  D,  and  can,  in  certain 
cases,  measure  to  fractions  of  an  ohm.  Fig.  216  shows  a 


CHAP,  vi  RESISTANCE   BRIDGES  419 

more  complete  scheme,  in  which  resistances  of  10,  100, 
and  1000  ohms  are  included  in  the  arms  A  and  C. 

Example.  —  Suppose  we  had  a  wire,  whose  resistance  we 
knew  to  be  between  46  and  47  ohms,  and  wished  to 
measure  the  fraction  of  an  ohm,  we  should  insert  it  at  D, 
and  make  A  100  ohms  and  C  10  ohms ;  in  that  case  D 
would  be  balanced  by  a  resistance  in  B  10  times  as  great 
as  the  wire  D.  If,  on  trial,  this  be  found  to  be  464  ohms, 
we  know  that  D  =  464  X  10  -r 100  =  46*4  ohms. 

415.  Other  Patterns  of  Bridge.  —  In  practice  the 
bridge  is  seldom  or  never  made  in  the  lozenge-shape  of 
the  diagrams. 

Post-Office  Bridge.  —  The  resistance-box  of  Fig.  215  is, 
in  itself,  a  complete  "  bridge  "  of  the  post-office  pattern, 
the  appropriate  connexions  being  made  by  screws  at 
various  points.  In  using  the  bridge  the  battery  circuit 
should  always  be  completed  by  depressing  the  key  Kj 
before  the  key  K2  of  the  galvanometer  circuit  is  depressed, 
in  order  to  avoid  the  sudden  violent  "  throw "  of  the 
galvanometer  needle,  which  occurs  on  closing  circuit  in 
consequence  of  self-induction  (Art.  458). 

Dial  Bridge.  —  To  avoid  errors  arising  from  the  differ- 
ent numbers  of  plugs  in  use,  the  coils  of  a  bridge  are 
sometimes  arranged  in  dials  —  the  units  in  one,  the  tens 
of  ohms  in  another,  and  so  forth  —  each  dial  having  but 
one  plug,  or  a  movable  arm  like  Fig.  206. 

Metre  Bridge.  —  This  is  a  simple  form  very  useful  for 
measuring  resistances  not  exceeding  a  few  hundred  ohms. 
Upon  a  long  board  is  stretched  over  a  scale  one  metre 
long  a  uniform  thin  wire  of  German-silver  or  other  alloy, 
its  ends  being  joined  to  stout  pieces  of  copper.  A,  B,  C, 
and  D  are  four  resistances  joined  as  shown  by  stout  strips 
of  copper.  When  the  wire  from  the  galvanometer  is  slid 
along  the  wire  to  such  a  point  that  there  is  no  current,  it 
follows  that 


420  ELECTRICITY  AND  MAGNETISM     PART  n 

Foster's  method  of  measuring  small  differences  of  resist- 
ance is  to  get  balance  at  a  certain  point  along  the  wire, 
then  interchange  A  and  B,  and  again  get  balance  at 
another  point.  The  resistance  of  the  piece  of  wire  be- 


B 


Fig.  217. 

tween  the  two  points  will  then  be  equal  to  the  difference 
of  the  resistances  A  and  B. 

*In  a  simpler  way  of  using  the  bridge,  A  and  B  are 
replaced  by  strips  of  no  appreciable  resistance,  so  that 

a  :  b : :  C  :  D. 

If  D  is  the  unknown  resistance  and  C  a  known  resist- 
ance, the  ratio  of  the  lengths  a  and  b  at  once  enables  the 
unknown  resistance  to  be  calculated. 

For  further  details  of  bridge  methods  consult  Gray's 
Absolute  Measurements  in  Electricity  and  Magnetism, 
Kempe's  Electrical  Measurement,  or  Ayrton's 
Practical  Electricity. 

416.  Measurement  of  Electromotive-Force.  —  There 
being  no  easy  absolute  method  of  measuring  electromo- 
tive-forces, they  are  usually  measured  relatively,  by  com- 
parison with  the  electromotive-force  of  a  standard  cell, 
such  as  Clark's  (Art.  188).  The  methods  of  comparison 
are  various;  only  five  are  here  mentioned. 

(a)  Reduced  Deflexion  Method.  —  Call  E  the  electro- 
motive-force of  the  battery  to  be  measured,  and  E'  that  of 
a  standard  battery.  Join  E  with  a  galvanometer,  and  let 
it  produce  a  deflexion  of  8t  degrees  through  the  resist- 


CHAP,  vi  POTENTIOMETER.  421 

ances  of  the  circuit ;  then  add  enough  resistance  r  to 
bring  down  the  deflexion  to  8.2  degrees  —  say  10  degrees 
less  than  before.  Now  substitute  the  standard  battery  in 
the  circuit  and  adjust  the  resistances  till  the  deflexion  is 
8L  as  before,  and  then  add  enough  resistance  r1  to  bring 
down  the  deflexion  to  82.  Then 

r':r  =  E' :  E, 

since  the  resistances  that  will  reduce  the  strength  of  the 
current  equally  will  be  proportional  to  the  electromotive- 
forces.  (Not  recommended.) 

(5)  Potentiometer  Method.  —  If  the  poles  of  a  standard 
battery  are  joined  by  a  long  thin  wire,  the  potential  will 
fall  uniformly  from  the  +  to  the  —  pole.  Hence,  by 


Fig.  218. 

making  contacts  at  one  pole  and  at  a  point  any  desired 
distance  along  the  wire,  any  desired  proportional  part  of 
the  whole  electromotive-force  can  be  taken.  This  pro- 
portional part  may  be  balanced  against  the  electromotive- 
force  of  any  other  battery  as  follows  :  —  Let  a  uniform 
thin  wire  of  platinoid  or  German-silver  be  stretched  over 
a  scale  divided  into  say  2000  parts.  Connect  a  Clark 
standard  cell  C  through  a  sensitive  galvanometer,  as 
shown  in  Fig.  218,  to  make  contact  at  the  1434  division 
of  the  scale.  Then  connect  a  single  accumulator  cell 
B,  or  two  Daniell's,  or  a  Grove  cell  with  a  sliding 
contact,  and  move  it  up  and  down  until  a  point  is  found 


422  ELECTRICITY  AND   MAGNETISM      PART  n 

such  that  the  galvanometer  shows  that  the  Clark  cell 
is  balanced.  Then  connect  the  cell  X  whose  E.M.F.  is 
to  be  measured,  and  slide  its  contact  along  the  wire 
until  it  also  is  balanced.  Suppose  it  balances  at  1024 
of  the  scale,  its  E.M.F.  will  be  1-024.  A  single  galvan- 
ometer will  suffice  if  the  wire  to  X  is  joined  in  between 
G  and  the  Clark  cell. 

(c)  Voltmeter   Method.  —  If  a  galvanometer  be  con- 
structed so  that  the   resistance   of  its  coils  is  several 
thousand  ohms  (in  comparison  with  which  the  internal 
resistance  of  a  battery  or  dynamo  machine  is  insignifi- 
cant), it  will  serve  to  measure  electromotive-forces ;  for 
the  strength  of  current  through  it  will  depend  only  on 
the   electromotive-force   between   the   ends   of  the  coil. 
(See  Art.  220  on  Voltmeters.) 

(d)  Condenser    Method.  —  A    condenser    of    known 
capacity  is  charged  from  a  standard  cell,  and  then  dis- 
charged through   a  ballistic  galvanometer  (Art.   218). 
The   cell  to  be   compared   is  then   substituted  for  the 
standard  cell.     The  E.M.F.  is  proportional  to  the  throw 
of  the  galvanometer. 

(e)  Electrometer    Method.  —  The    electromotive-force 
of  a  battery  may  be  measured  directly  as  a  difference  of 
potentials  by  a  quadrant  electrometer.      In  this  case  the 
circuit  is  never  closed,  and  no  current  flows. 

417.   Measurement  of  Internal  Resistance  of  Cells.  — 
This  may  be  done  in  several  ways. 

(a)  Condenser    Method.  —  As    in    (d)    of    preceding 
Article,  observe  throw  of  galvanometer  from  condenser 
charged  by  the  cell.     Then  shunt  the  cell  with  a  suitably 
high  resistance  R  and  take  another  charge  and  discharge. 
If  the  two  throws  are  called  dl  and  f/2,  the  internal  resist- 
ance will  be  =  R(</j  —  d^)/dy 

(b)  Half-deflexion  Method.  —  Place  the  cell  in   series 
with  a  galvanometer  the  resistance  of  which  is  G,  and  a 
resistance-box  in  which  there  is  unplugged  a  resistance  li 
such  that  the  deflexion  is  conveniently  large.       Now  in- 


CHAP,  vi      METHODS   OF   MEASUREMENT  423 

crease  the  resistance  in  the  box  until  it  is  seen  by  the 
deflexion  that  the  current  has  been  reduced  to  half 
what  it  was.  If  this  added  resistance  is  called  a,  then 
by  Ohm's  law  it  follows  that  the  internal  resistance  is 
—  a  —  (R  +  G).  This  method  is  suitable  for  very  high 
internal  resistances. 

(c)  Method  of  Opposition.  —  Take  two  similar  cells 
and  join  them  in  opposition  to  one  another,  so  that  they 
send  no  current  of  their  own.  Then  measure  their 
united  resistance  just  as  the  resistance  of  a  wire  is 
measured.  The  resistance  of  one  cell  will  be  half  that 
of  the  two. 

(</)  Mance^s  Method.  —  Place  the  cell  itself  in  one 
arm  of  the  Wheatstone's  bridge,  and  put  a  key  where 
the  battery  usually  is,  adjust  the  resistances  till  the 
permanent  galvanometer  deflexion  is  the  same  whether 
the  key  be  depressed  or  not.  When  this  condition 
of  things  is  attained  the  battery  resistance  is  balanced 
by  those  of  the  other  three  arms.  (Not  a  reliable 
method.) 

(e)  Alternate  Current  Method.  —  If  greater  accuracy  is 
required  in  the  opposition  method,  the  cells  in  opposition 
may  be  placed  in  one  of  the  arms  of  a  Wheatstone's  bridge 
in  which  instead  of  the  usual  battery  is  inserted  the  sec- 
ondary coil  of  a  small  induction  coil  (without  condenser), 
and  with  which  a  telephone  receiver  is  used  instead 
of  a  galvanometer.  The  ceasing  of  the  buzzing  in  the 
telephone  corresponds  to  nul  deflexion.  By  this  means 
we  avoid  the  disturbance  of  the  balance  of  the  opposing 
cells  which  occurs  if  continuous  currents  are  used.  This 
method  is  also  excellent  for  measuring  resistances  of 
liquids. 

418.  Measurement  of  Capacity.  —  The  capacity  of  a 
condenser  may  be  measured  by  comparing  it  with  the 
capacity  of  a  standard  condenser  —  such  as  the  i  micro- 
farad condenser  (Fig.  159)  —  in  one  of  the  following 
ways :  — 


424  ELECTRICITY  AND   MAGNETISM      PART  n 

(a)  Electrometer  Method.  —  Charge  the  condenser  of 
unknown  capacity  to  a  certain  potential;  then  make  it 
share  its  charge  with  the  condenser  of  known  capacity, 
and  measure  the  potential  to  which  the  charge  sinks; 
then  calculate  the  original  capacity,  which  will  bear  the 
same  ratio  to  the  joint  capacity  of  the  two  as  the  final 
potential  bears  to  the  original  potential. 

(b)  Ballistic  Galvanometer  Method.  —  Charge  each  con- 
denser to  equal  differences  of  potential  from  the  same  cell 
or  battery,  and  then  discharge  each  successively  through 
a  ballistic  galvanometer  (Art.  188).     The  throw  of  the 
needle  will  be  proportional  in  each  case  to  the  charge, 
and  therefore  to  the  capacity. 

The  law  of  the  ballistic  galvanometer  is  :  — 
KV  =  Q  =  -X  -sin*a, 

G       n 

where  Q  is  the  quantity  of  electricity  (in  C.G.S.  units),  H  the 
magnetic  field,  by  the  constant  of  the  galvanometer,  T  the 
period  of  one  complete  swing  of  the  needle,  and  «  the  angle 
of  first  swing.  The  factor  H/G  may  be  eliminated  by  passing  a 
steady  current  C  to  produce  a  steady  deflexion  /3  ;  when 


G 
Combining  this  with  the  preceding,  we  have 

_  CT  sin  £  * 
y~    TT  tan/3 

If  «  and  ft  are  both  small  this  becomes 

Q  =  CTa/27T/3. 

If  C  is  in  amperes,  Q  will  be  in  coulombs. 

(c)  Bridge  Method.  —  Connect  the  two  condensers  K, 
and  K2  in  two  arms  of  a  Wheatstone's  bridge  and  adjust 


CHAP,  vi      MEASUREMENT  OF   CAPACITY  425 

the  resistances  so  that  there  is  no  deflexion  on  charge  or 
discharge  (Fig.  219).  Then  Kj :  K2: :  ra:r,,  the  larger 
capacity  acting  as  a  smaller  resistance. 

(d)  Potential-divider  nul  Method.  —  Two  resistances  i\ 
and  r2  are  joined  in  series  to  the  +  and  —  poles  of  a 
battery.  The  middle  point  between  r}  and  r2  is  connected 
to  one  of  the  terminals  of  l\l  and  also  of  K2.  The  free 


ilH 

Fig.  219. 

terminals  of  Kx  and  K2  are  momentarily  joined  to  the  + 
and  —  poles  of  the  battery  respectively  and  receive  charges 
of  opposite  sign.  They  are  then  connected;  and  if  of 
equal  amount  the  charges  will  neutralize  each  other.  The 
resistances  rl  and  r2  are  adjusted  until  this  condition  is 
satisfied,  as  shown  by  nul  deflexion  when  the  key  of  a 
galvanometer  circuit  across  their  terminals  is  depressed. 
Then  Kt :  K2 : :  r2 :  rr 

(e)  Tuning-fork  Method.  —  A  tuning-fork  acting  as  a 
vibrating  two-way  switch  charges  and  discharges  the  con- 
denser n  times  per  second,  allowing  to  pass  VKn  coulombs 
per  second  or  VKn  amperes.  The  apparent  resistance  r 
of  this  combination  is  1/Kn,  and  can  be  measured  by  a 
Wheatstone  bridge,  whence  K  =  1/nr. 

(/)  Loss  of  Charge  Method.  —  This  is  the  same  as  the 
last  method  in  Art.  411e,  a  known  high  resistance  being 
used. 


CHAPTER  VII 

THERMO-ELECTRICITY 

LESSON  XXXV.  —  Thermo-Electric  Currents 

419.  Seebeck  Effect.  —  In  1822  Seebeck  discovered 
that  a  current  may  be  produced  in  a  closed  circuit  by 
heating  a  point  of  contact  of  two  dissimilar  metals.     If 
a  piece  of  bismuth  and  a  piece  of  antimony  be  soldered 
together,  and  their  free  ends  connected  with  a  short-coil 
galvanometer,  it  is  found  that  if  the  junction  be  wanned 
to  a  temperature  higher  than  that  of  the  rest  of  the  cir- 
cuit, a  current  flows  in  the  direction  from  bismuth  to 
antimony  across  the  heated  point ;  the  current  being  pro- 
portional to  the  excess  of  temperature.     If  the  junction 
is  cooled  below  the  temperature  of  the  rest  of  the  circuit 
a  current  in  the   opposite   direction   is  observed.     The 
electromotive-force  thus  set  up  will  maintain  the  current 
so  long  as  the  excess  of  temperature  of  the  heated  point 
is  kept  up ;  heat  being  all  the  while  absorbed  in  order  to 
maintain  the  energy  of  the  current.     Such  currents  are 
called   Thermo-electric   currents,  and  the   electromotive- 
force  producing  them  is  known  as   Thermo-electromotive- 
force. 

420.  Peltier  Effect.  —  In   1834   Peltier    discovered 
a  phenomenon  which  is  the  converse  of  that  discovered 
by  Seebeck.     He  found  that  if  a  current  of  electricity 
from  a  battery  be  passed  through  a  junction  of  dissimilar 

420 


CHAP,  vii      THERMO-ELECTRIC   EFFECTS  427 

metals  the  junction  is  either  heated  or  cooled,  according 
to  the  direction  of  the  current.  Thus  a  current  which 
passes  through  a  bismuth-antimony  pair  in  the  direction 
from  bismuth  to  antimony  absorbs  heat  in  passing  the 
junction  of  these  metals,  and  cools  it;  whereas,  if  the 
current  flow  from  antimony  to  bismuth  across  the  junc- 
tion it  evolves  heat,  and  the  junction  rises  in  tempera- 
ture. It  is  clear  that  if  bismuth  is  positive  with  respect 
to  antimony,  any  current  that  may  be  caused  to  flow 
from  bismuth  to  antimony  is  aided  by  the  electromotive- 
force  at  that  junction ;  whilst  any  current  flowing  from 
antimony  to  bismuth  will  meet  with  an  opposing  electro- 
motive-force. In  the  latter  case  the  current  will  do  work 


Fig.  220. 

and  heat  the  junction ;  in  the  former  the  current  will 
receive  energy  at  the  expense  of  the  junction,  which  will 
give  up  heat.  In  Fig.  220,  the  feathered  arrows  at  the 
junctions  represent  the  Peltier  electromotive-forces,  and 
the  plain  arrows  the  direction  of  the  current. 

This  phenomenon  of  heating  (or  cooling)  by  a  current, 
where  it  crosses  the  junction  of  two  dissimilar  metals 
(known  as  the  "Peltier  effect,"  to  distinguish  it  from  the 
ordinary  heating  of  a  circuit  where  it  offers  a  resistance 
to  the  current,  which  is  sometimes  called  the  "Joule 
effect "),  is  utterly  different  from  the  evolution  of  heat 
in  a  conductor  of  high  resistance,  for  (a)  the  Peltier  effect 
is  reversible ;  the  current  heating  or  cooling  the  junction 
according  to  its  direction,  whereas  a  current  meeting  with 
resistance  in  a  thin  wire  heats  it  in  whichever  direction 
it  flows ;  and  (b)  the  amount  of  heat  evolved  or  absorbed 
in  the  Peltier  effect  is  proportional  simply  to  the  current, 
not  to  the  square  of  the  current  as  the  heat  of  resist- 
ance is. 


428  ELECTRICITY  AND  MAGNETISM     PART  n 

The  complete  law  of  the  heat  developed  in  a  circuit 
will  therefore  require  to  take  into  account  any  Peltier 
effects  which  may  exist  at  metal  junctions  in  the  circuit. 
If  the  letter  P  stand  for  the  difference  of  potential  due 
to  the  heating  of  the  junction,  expressed  as  a  fraction  of 
a  volt,  then  the  complete  law  of  heat  is 


=  0-24x 


which  the  student  should  compare  with  Joule's  law  in 
Art.  427.  The  quantity  called  P  is  also  known  as  the 
coefficient  of  the  Peltier  effect ;  it  has  different  values  for 
different  pairs  of  metals,  and  is  numerically  equal  to  the 
number  of  ergs  of  work  which  are  evolved  as  heat  at  a 
junction  of  the  particular  metals  by  the  passage  of  one 
absolute  unit  (10  coulombs)  of  electricity  through  the 
junction. 

421.    Thermo-electric    Laws.  —  The    thermo-electric 
properties  of  a  circuit  are  best  studied  by  reference  to 

the  simple  circuit 
of  Fig.  221,  which 
represents  a  bis- 
muth -  antimony 
pair  united  by  a 
copper  wire.  If 
all  parts  of  the 
circuit  are  at  one 
temperature,  even 
though  there  may 
be  at  the  junc- 
tions electromo- 
tive-forces as  suggested  above,  there  will  be  no  current, 
since  the  electromotive-forces  are  in  equilibrium.  But 
when  a  junction  is  heated  this  equilibrium  no  longer 
exists,  and  there  will  be  a  resultant  electromotive-force. 
It  is  found  to  obey  the  following  laws  :  — 


CHAP,  vii      THERMO-ELECTRIC  POWER  429 

(i.)  The  thermo-electromotive-force  is,  for  the  same  pair 
of  metals,  proportional  (through  limited  ranges  of 
temperature)  to  the  excess  of  temperature  of  the 
junction  over  the  rest  of  the  circuit. 

(ii.)  The  total  thermo-electromotive-force  in  a  circuit  is  the 
algebraic  sum  of  all  the  separate  thermo-electromotive- 
forces  in  the  various  parts. 

It  follows  from  this  law  that  the  various  metals  can  be 
arranged,  as  Seebeck  found,  in  a  series,  according  to  their 
thermo-electric  power,  each  one  in  the  series  being  thermo- 
electrically  positive  (as  bismuth  is  to  antimony)  toward 
one  lower  down. 

422.  Thermo-electric  Power.  —  In  the  following  table 
is  shown  the  thermo-electric  series  of  metals,  together  with 
the  thermo-electric  power  of  each  when  cold.  The  term 
thermo-electric  power  of  a  metal  means  the  electromotive- 
force  per  degree  (centig.)  for  a  pair  made  of  that  metal 
with  the  standard  metal  (lead).  In  the  table  the  numbers 
are  microvolts  per  degree. 

+  Bismuth     .        .        .        .          89  to  97 

Nickel        ....          22 

German-silver  .        .        .          H'75 

Lead 0 

Platinum   .        .        .  -  0*9 

Copper       ....  -   1-36 

Zinc -   2'3 

Iron — 17*5 

—  Antimony.        .        .        .  —  22'6  to  —  26*4 

Tellurium          ...  502 

Selenium    ....  800 

A  very  small  amount  of  impurity  may  make  a  great 
difference  in  the  thermo-electric  power  of  a  metal,  and 
some  alloys,  and  some  of  the  metallic  sulphides,  as  galena, 
exhibit  extreme  thermo-electric  power. 

The  electromotive-forces  due  to  heating  single  pairs 
of  metals  are  very  small  indeed.  If  the  junction  of  a 
copper-iron  pair  be  raised  1°  C.  above  the  rest  of  the 
circuit  its  electromotive-force  is  only  15-14  microvolts. 


430  ELECTRICITY   AND   MAGNETISM      PART  n 

That  of  the  more  powerful  bismuth-antimony  pair  is 
for  1°  C.,  about  117  microvolts.  Thermo-electric  power 
varies,  however,  with  temperature :  for  example,  that  of 
iron  is  really  —  17-5  +  0-049^  (where  t  is  the  mean  tem- 
perature of  the  two  junctions),  iron  becoming  less  nega- 
tive when  hot.  Copper  is  —  1-36  —  0-Olf,  becoming  more 
negative.  There  will  be  obviously  one  particular  tem- 
perature or  neutral  point,  at  which  their  powers  will  be 
equal. 

423.  Thermo-electric  Inversion.  —  Gumming  discov- 
ered   that    in   the    case    of   iron    and    other   metals   an 
inversion   of  their   thermo-electric  properties  may  take 
place  at  a  high  temperature.     In  the  case  of  the  copper- 
iron  pair  the  temperature  of  275°  is  a  neutral  point ; 
below  that  temperature  the  current  flows  through   the 
hotter  junction  from  the  copper  to  the  iron ;    but  when 
the  circuit  is   above   that  temperature  iron  is  thermo- 
electrically  positive  to  copper.     The  neutral  point  for  a 
zinc-iron   pair  is   about  200°.     The   inversion   is  easily 
shown  by  heating  the  junction  of  two  long  strips  of  these 

metals,    riveted    together    in    a 
V-form,  and  watching  the  effect 
on  a  galvanometer  connected  to 
their    other    ends.     There    will 
at   first    be    a    deflexion    which 
will  go  on  increasing  until  the 
temperature  of  200°  is  attained, 
but  on  further  heating  the  junc- 
°°     lo°"    200°  300°  *°°°c      tion  the  deflexion  diminishes  and 
at  about  400°  reverses,  the  cur- 
rent flowing  the  other  way.     Fig.  222  shows  graphically 
the  curves  obtained  with  iron-zinc  and  iron-copper  pairs 
when  one  junction  is  kept  at  0°  while  the  other  is  heated. 
The  dotted  line  is  for  the  iron-zinc  pair  when  one  junction 
is  kept  at  50°  and  the  other  heated. 

424.  Thermo-electric     Diagram.  —  The     facts      of 
thermo-electricity    are   best  studied    by   means    of    the 


CHAP,  vii     THERMO-ELECTRIC   DIAGRAM 


431 


diagrams  suggested  by  Lord  Kelvin  and  constructed  by 
Professor  Tait.  In  that  given  in  Fig.  223  the  horizontal 
divisions  represent  the  temperatures ;  the  vertical  dis- 
tances indicating  the  thermo-electric  power,  in  microvolts 
per  degree.  These  powers  are  measured  with  respect  to 
the  metal  lead,  which  is  taken  as  the  standard  of  zero  at 
all  temperatures,  because,  while  with  other  metals  there 


Fig.  223. 

appears  to  be  a  difference  of  potentials  between  the  metal 
hot  and  the  same  metal  cold,  hot  lead  brought  into  contact 
with  cold  lead  shows  no  perceptible  thermo-electric  differ- 
ence. 

An  example  will  illustrate  the  usefulness  of  the  dia- 
gram. Let  a  circuit  be  made  by  uniting  at  both  ends  a 
piece  of  iron  and  a  piece  of  copper;  and  let  the  two 
junctions  be  kept  at  0°  and  100°  respectively  by  melting 
ice  and  boiling  water.  Then  the  total  electromotive-force 
round  the  circuit  is  represented  by  the  area  a,  0,  —  15,  b. 


432  ELECTRICITY   AND  MAGNETISM       PART  11 

The  slope  of  the  lines  for  the  various  metals  represents 
the  property  referred  to  above,  of  an  electromotive-force 
between  differently-heated  portions  of  the  same  metal 
accompanied  by  an  absorption  or  evolution  of  heat  when 
the  current  flows  from  a  hotter  to  a  colder  portion  of  the 
same  metal.  This  effect,  known  as  the  Thomson  effect 
from  its  discoverer  Sir  W.  Thomson  (Lord  Kelvin),  is 
opposite  in  iron  to  what  it  is  in  copper  or  zinc.  Copper 
when  hot  is  negative  compared  with  copper  that  is  cold. 
Hence  if  a  current  is  sent  from  a  hot  to  a  cold  part  of  a 
piece  of  copper  it  encounters  an  opposing  electromotive- 
force.  Hence  when  a  current  of  electricity  flows  from  a 
hot  to  a  cold  point  in  copper  it  evolves  heat;  and  it 
absorbs  heat  when  it  flows  from  a  cold  point  to  a  hot 
point  in  the  copper.  In  iron  a  current  flowing  from  a 
hot  point  to  a  cold  point  absorbs  heat. 

The  thermo-electromotive-force  of  a  pair,  of  which 
the  junctions  are  at  temperatures  T  and  t  respectively, 
and  of  which  n  is  the  temperature  of  the  neutral  point, 
may  be  conveniently  expressed  by  the  following  formula:  — 


where  p  is  the  volts  per  degree  (at  0°)  as  given  in  the 
table  (Art.  422). 

425.  Thermo-electric  Piles.  —  The  electromotive- 
force  of  a  bismuth-antimony  pair,  when  the  junctions  are 
kept  at  0°  and  100°,  is  only  0-0115  volt.  In  order  to 
increase  the  electromotive-force  of  thermo-electric  pairs 
it  is  usual  to  join  a  number  of  pairs  of  metals  (preferably 
bismuth  and  antimony)  in  series,  but  so  bent  that  the 
alternate  junctions  can  be  heated  as  shown  in  Fig.  224  at 
BBB,  whilst  the  other  set  AAA  are  kept  cool.  The 
various  electromotive-forces  then  all  act  in  the  same 
direction,  and  the  current  is  increased  in  proportion  to 
the  number  of  pairs  of  junctions.  Powerful  thermo- 
electric batteries  have  been  made  bv  Clamond  —  an  iron- 


CHAP,  vii  THERMOPILES  433 

galena  battery  of  120  pairs  affording  a  strong  current ; 
but  it  is  extremely  difficult  to  maintain  them  in  effective 
action  for  long,  as  they  fail  after  continued  use,  probably 
owing  to  a  permanent  molecular  change  at  the  junctions. 
In  the  hands  of  Melloni  the  thermo-electric  pile  or  ther- 
mopile, constructed  of  many  small  pairs  of  antimony 
and -bismuth  united  in  a  compact  form,  proved  an  ex- 
cellent electrical  thermometer  when  used  in  conjunction 
with  a  sensitive  short-coil  astatic  galvanometer.  For  the 


Fig.  224. 

detection  of  excessively  small  differences  of  temperature 
the  thermopile  is  an  invaluable  instrument,  the  currents 
being  proportional  to  the  difference  of  temperature 
between  the  hotter  set  of  junctions  on  one  face  of  the 
thermopile  and  the  cooler  set  on  the  other  face.  The 
arrangement  of  a  thermopile  with  the  old  astatic  galvan- 
ometer is  shown  in  Fig.  2-o. 

A  still  more  sensitive  arrangement  for  detecting 
minute  heating  due  to  radiation  consists  in  suspending 
between  the  poles  of  a  powerful  magnet  a  closed  circuit 
having  a  bismuth-antimony  junction  in  it.  Sturgeon 


434 


ELECTRICITY  AND   MAGNETISM      PART  n 


proposed     a    thermo  -  galvanometer    on     this     plan    in 
1835. 

In  the  radio-micrometer  of  Veruon  Boys  (1880)  a  loop 
of  wire,  suspended  by  a  delicate  quartz  fibre  between  the 


poles  of  a  magnet  (like  the  coil  in  Fig.  126)  has  its  circuit 
closed  at  its  lower  end  by  a  piece  of  antimony  and  a 
piece  of  bismuth  (or  alloys  of  these  metals)  soldered  to  a 
minute  disk  of  copper  foil.  A  rise  of  temperature  of  the 
copper  foil  even  so  small  as  one  millionth  of  a  degree  will 
generate  a  current  in  the  loop  and  give  a  deflexion  over 
one  division  of  the  scale.  With  an  instrument  of  this 
kind  the  radiant  heat  of  a  candle  can  be  detected  at  a 
distance  of  two  miles. 


CHAPTER  VIII 

HEAT,    POWER,    AND    LIGHT,    FROM    ELECTRIC    CURRENTS 

LESSON  XXXVI.  —  Heating  Effects  of  Currents 

426.  Heat  and  Resistance.  —  A  current  may  do 
work  of  various  kinds,  chemical,  magnetic,  mechanical, 
and  thermal.  In  every  case  where  a  current  does  work 
that  work  is  done  by  the  expenditure  of  part  of  the 
energy  of  the  current.  We  have  seen  that,  by  the  law  of 
Ohm,  the  current  produced  by  a  given  battery  is  dimin- 
ished in  strength  by  anything  that  increases  the  external 
resistance.  But  the  current  may  be  diminished,  in 
certain  cases,  by  another  cause,  namely,  the  setting  up 
of  an  opposing  electromotive-force  at  some  point  of  the 
circuit.  Thus,  in  passing  a  current  through  an  electro- 
lytic cell  (Art.  237)  there  is  a  diminution  due  to  the 
opposing  electromotive-force  ("  polarization ")  which  is 
generated  while  the  chemical  work  is  being  done.  So, 
again,  when  a  current  is  used  to  drive  an  electric  motor 
(Art.  443),  the  rotation  of  the  motor  will  itself  generate 
a  back  E.M.F.,  which  will  diminish  the  current.  What- 
ever current  is,  however,  not  expended  in  this  way  in 
external  work  is  frittered  down  into  heat,  either  in  the 
battery  or  in  some  part  of  the  circuit,  or  in  both.  Suppose 
a  quantity  of  electricity  to  be  set  flowing  round  a  closed 
circuit.  If  there  were  no  resistance  to  stop  it  it  would 
circulate  for  ever ;  just  as  a  waggon  set  rolling  along  a 
435 


ELECTRICITY   AND   MAGNETISM      PART  n 


circular  railway  should  go  round  for  ever  if  it  were  not 
stopped  by  friction.  When  matter  in  motion  is  stopped 
by  friction  the  energy  of  its  motion  is  frittered  down  by 
the  friction  into  heat.  When  electricity  in  motion  is 
stopped  by  resistance  the  energy  of  its  flow  is  frittered 
down  by  the  resistance  into  heat.  Heat,  in  fact,  appears 
wherever  the  circuit  offers  a  resistance  to  the  current. 
If  the  terminals  of  a  battery  be  joined  by  a  short  thick 
wire  of  small  resistance,  most  of  the  heat  will  be  de- 
veloped in  the  battery  and  so  wasted ;  whereas,  if  a  thin 
wire  of  relatively  considerable  resistance  be  interposed  in 
the  outer  circuit,  it  will  grow  hot,  while  the  battery  itself 
will  remain  comparatively  cool. 

427.   Laws  of  Development  of  Heat:  Joule's  Law. — 
To  investigate  the  development  of  heat   by  a  current, 

Joule  and  Lenz  used  in- 
struments on  the  principle 
shown  in  Fig.  226.  A 
thin  wire  joined  to  two 
stout  conductors  is  en- 
closed within  a  glass  vessel 
containing  alcohol,  into 
which  also  a  thermometer 
dips.  The  resistance  of 
the  wire  being  known,  its 
relation  to  the  other  resist- 
ances can  be  calculated. 
Joule  found  that  the  num- 
ber of  units  of  heat  developed 
in  a  conductor  is  proportional  — 
(i.)  to  its  resistance ; 
(ii.)  to  the  square  of  the  strength  of  the  current ; 

and 

(iii.)  to  the  time  that  the  current  lasts. 
The  equation  expressing  these  relations  is  known  as 
Joule's  Law,  and  is  — 

U  =  C2R*  x  0-24, 


Fig.  226. 


CHAP,  vin  JOULE'S  LAW  437 

where  C  is  the  current  in  amperes,  R  the  resistance  in 
ohms,  /  the  time  in  seconds,  and  U  the  heat  in  calories ; 
one  calorie  being  the  amount  of  heat  that  will  raise 
1  gramme  of  water  through  1°  C.  of  temperature 
(Art.  281). 

This  equation  is  equivalent  to  the  statement  that  a 
cwrent  of  one  ampere  flowing  through  a  resistance  of  one 
ohm  developes  therein  O24  calories  per  second.  The  proof 
of  this  rule  is  given  in  Art.  439.  The  heat  produced 
thus  by  the  degradation  of  energy  in  a  resistance  is 
sometimes  called  the  "  ohmic  "  heat  to  distinguish  it 
from  the  reversible  Peltier  effect  (Art.  420). 

The  electric  unit  of  heat,  the  joule,  is  only  0-24  of  an 
ordinary  heat-unit  or  calorie,  and  1  calorie  will  be  equal 
to  4-2  joules. 

The  second  of  the  above  laws,  that  the  heat  is,  cceteris 
paribus,  proportional  to  the  square  of  the  strength  of  the 
current,  often  puzzles  young  students,  who  expect  the 
heat  to  be  proportional  to  the  current  simply.  Such 
may  remember  that  the  consumption  of  zinc  is,  cceteris 
parilus,  also  proportional  to  the  square  of  the  current ; 
for,  suppose  that  in  working  through  a  high  resistance 
(so  as  to  get  all  the  heat  developed  outside  the  battery) 
we  double  the  current  by  doubling  the  number  of  battery 
cells,  there  will  be  twice  as  much  zinc  consumed  as  before 
in  each  cell,  and  as  there  are  twice  as  many  cells  as  at 
first  the  consumption  of  zinc  is  four  times  as  great  as 
before. 

428.  Favre's  Experiments. — Favre  made  a  series  of  most 
important  experiments  on  the  relation  of  the  energy  of  a  current 
to  the  heat  it  developes.  He  ascertained  that  the  number  of 
calories  evolved  when  33  grammes  (1  equivalent)  of  zinc  are 
dissolved  in  dilute  sulphuric  acid  (from  which  it  causes  hydro- 
gen to  be  given  off)  is  18,682.  This  figure  was  arrived  at  by 
conducting  the  operation  in  a  vessel  placed  in  a  cavity  of  his 
calorimeter,  an  instrument  resembling  a  gigantic  thermometer 
filled  with  mercury,  the  expansion  of  which  was  proportional  to 
the  heat  imparted  to  it.  When  a  Smee's  cell  was  introduced  into 


438  ELECTRICITY  AND   MAGNETISM       PART  n 


the  same  instrument,  the  solution  of  the  same  amount  of  zinc 
was  observed  to  be  accompanied  by  the  evolution  of  18,674  calo- 
ries (i.e.  an  amount  almost  identical  with  that  observed  before), 
and  this  amount  was  the  same  whether  the  evolution  took  place 
in  the  battery-cell  when  the  circuit  was  closed  with  a  short  thick 
wire,  or  whether  it  took  place  in  a  long  thin  wire  placed  in  the 
external  circuit.  He  then  arranged  5  Smee's  cells  in  series,  in 
cavities  of  the  calorimeter,  and  sent  their  current  round  a  small 
electric  motor.  The  amount  of  heat  evolved  during  the  solution 
of  33  grammes  of  zinc  was  then  observed  in  three  cases :  (i.)  when 
the  motor  was  at  rest;  (ii.)  when  the  motor  was  running  round 
and  doing  no  work  beyond  overcoming  the  friction  of  its  pivots ; 
(iii.)  when  the  motor  was  employed  in  doing  13,124,000  gramme- 
centimetres  (=  12,874  X  106  ergs)  of  work,  by  raising  a  weight 
by  a  cord  running  over  a  pulley.  The  amounts  of  heat  evolved 
in  the  circuit  in  the  three  cases  were  respectively,  18,067, 18,657, 
and  18,374  calories.  In  the  last  case  the  work  done  accounts  for 
the  diminution  in  the  heat  wasted  in  the  circuit.  If  we  add  the 
heat-equivalent  of  the  work  done  to  the  heat  evolved  in  the 
latter  case,  we  ought  to  get  the  same  value  as  before.  Dividing 
the  12,874  X  106  ergs  of  work  by  Joule's  equivalent  (42  X  106), 
we  get  as  the  heat-equivalent  of  the  work  done  306  calories. 
Now  18,374  +  306  =  18,680,  a  quantity  which  is  almost  identical 
with  that  of  the  first  observation,  and  quite  within  the  limits  of 
unavoidable  experimental  error. 

429.  Rise  of  Temperature.  —  The  elevation  of  tem- 
perature in  a  resisting  wire  depends  on  the  nature  of  the 
resistance.  A  very  short  length  of  a  very  thin  wire  may 
resist  just  as  much  as  a  long  length  of  stout  wire.  Each 
will  cause  the  same  number  of  units  of  heat  to  be  evolved, 
but  in  the  former  case,  as  the  heat  is  spent  in  warming  a 
short  thin  wire  of  small  mass,  it  will  get  very  hot, 
whereas  in  the  latter  case  it  will  perhaps  only  warm  to 
an  imperceptible  degree  the  mass  of  the  long  thick  wire, 
which,  moreover,  has  a  larger  surface  to  get  rid  of  its 
heat.  If  the  wire  weigh  w  grammes,  and  have  a  specific 
capacity  for  heat  s,  then  U  =  swO,  where  6  is  the  rise  of 
temperature  in  degrees  (Centigrade).  Hence  if  none  of 
the  heat  were  radiated  away 

0  =  0-24 


CHAP,  viii         RISE   OF   TEMPERATURE  439 

Since  the  resistance  of  metals  increases  as  they  rise  in 
temperature,  a  thin  wire  heated  by  the  current  will  resist 
more,  and  grow  hotter  and  hotter  until  its  rate  of  loss  of 
heat  by  conduction  and  radiation  into  the  surrounding  air 
equals  the  rate  at  which  heat  is  supplied  by  the  current. 

The  following  pretty  experiment  illustrates  the  laws 
of  heating.  The  current  from  a  few  cells  is  sent  through 
a  chain  made  of  alternate  links  of  silver  and  platinum 
wires.  The  platinum  links  glow  red-hot  while  the  silver 
links  remain  comparatively  cool.  The  explanation  is 
that  the  specific  resistance  of  platinum  is  about  six  times 
that  of  silver,  and  its  capacity  for  heat  about  half  as 
great ;  hence  the  rise  of  temperature  in  wires  of  equal 
thickness  traversed  by  the  same  current  is  roughly  twelve 
times  as  great  for  platinum  as  for  silver. 

Thin  wires  heat  much  more  rapidly  than  thick,  the 
rise  of  temperature  in  different  parts  of  the  same  wire 
(carrying  the  same  current)  ivould  be,  for  different  thick- 
nesses, inversely  proportional  to  the  fourth  power  of  the 
diameters  if  they  had  equal  surfaces  for  radiation. 

Thus,  suppose  a  wire  at  any  point  to  become  reduced 
to  half  its  diameter,  the  cross-section  will  have  an  area 
\  as  great  as  in  the  thicker  part.  The  resistance  here 
will  be  4  times  as  great,  and  the  number  of  heat  units 
developed  will  be  4  times  as  great  as  in  an  equal*  length 
of  the  thicker  wire.  But  4  times  the  amount  of  heat 
spent  on  \  the  amount  of  metal  would  warm  it  to  a 
degree  16  times  as  great :  and  the  thin  wire  has  only  half 
as  much  surface  for  getting  rid  of  heat.  But  the  hotter  a 
body  becomes  the  more  freely  does  it  radiate  heat  to 
things  around  it.  For  wires  of  given  material,  the  current 
needed  to  raise  them  to  an  equal  temperature  varies  as 
the  square  root  of  the  cube  of  the  diameter.  This  law 
applies  to  the  sizes  of  wires  used  as  safety-fuses  in  electric 
lighting.  These  are  pieces  of  tin  wire  interposed  in  the 
circuit  to  melt  if  by  any  chance  the  current  becomes  abnor- 
mally strong. 


440  ELECTRICITY   AND   MAGNETISM        PART  n 

430.  Cardew's  Voltmeter.  —  The  current  flowing 
through  a  long  thin  wire  of  platinum  when  it  is  made  to 
connect  two  points  on  a  circuit  will  measure 
the  potential  difference  between  these  two 
points.  Owing  to  its  becoming  warmed  it 
will  expand,  and  its  expansion  may  be  made 
to  move  a  hand  over  a  dial  graduated  to 
read  volts  (Fig.  227). 

431.  Electric  Cautery. — For  surgical  pur- 
poses a  thin  platinum  wire,  heated  red-hot 
by  a  current,  is  sometimes  used  instead  of  a 
knife,  as,  for  example,  in  the  operation  of 
amputating  the  tongue  for  cancer.    Platinum 
is  chosen  on  account  of  its  iiifusibility,  but 
even  platinum  wires  are  fused  by  the  current 
if  too  strong.     Carbon  alone,  of  conductors, 
resists  fusion. 

432.  Blasting   by  Electricity.  —  In  con- 
sequence    of    these    heating    effects,     elec- 
tricity can  be  applied  in  blasting  and  mining 
to  ignite    the    charges.      Stout    conducting 

Fig.  227.  wires  are  carried  from  an  appropriate 
battery  at  a  distance  to  a  special  fuze,  in 
which  a  very  thin  platinum  wire  is  joined  in  the  circuit. 
This  wire  gets  hot  when  the  current  flows,  and  being- 
laid  amidst  an  easily  combustible  substance  to  serve 
as  a  priming,  ignites  this  and  sets  fire  to  the  charge 
of  gunpowder.  Torpedoes  can  thus  be  exploded 
beneath  the  water,  and  at  any  desired  distance  from 
the  battery. 

433.  Electric  Welding.  — If  two  wires  or  rods  of 
metal  are  held  together  with  sufficient  force  while  a  very 
large  current  is  passed  through  them,  much  heat  is 
developed  at  the  junction,  so  that  they  soften  and  become 
welded  together.  The  processes  of  electric  welding  have 
been  perfected  by  Elihu  Thomson,  who  has  utilized  for 
this  purpose  alternate-current  transformers  (Art.  480)  to 


CHAP,  vin  ELECTRIC   ENERGY  441 

produce  currents  of  many  hundred  amperes  at  a  pressure 
of  a  few  volts. 

A  singular  effect  is  noticed  when  two  iron  rods 
connected  to  the  poles  of  a  powerful  source  at  50  or 
more  volts  are  dipped  into  water.  The  rod  which  serves 
as  kathode  is  observed  to  be  covered  with  a  luminous 
layer,  and  it  presently  becomes  red-hot.  Guthrie,  who 
first  investigated  this  phenomenon  in  1876,  ascribed  the 
heating  to  the  resistance  of  a  film  of  hydrogen.  Recently 
it  has  been  made  the  basis  of  a  welding  method. 

434.  Electric  Cooking.  —  Since  public  supplies  of 
electricity  became  common,  electric  stoves,  ovens,  and 
heaters  for  cooking,  stewing,  etc.,  have  become  articles 
of  commerce.  The  heating  is  effected  by  passing  cur- 
rents through  resistance  wires  embedded  in  cement  or 
other  suitable  insulating  material. 


LESSON  XXXVII.  —  Electric  energy:   its  Supply  and 
Measurement 

435.  Electric  Energy.  —  An  electric  current  conveys 
energy  from  a  battery  or  dynamo  to  some  other  part 
of  the  circuit,  where  it  is  transformed  back  into  work, 
—  mechanical,  chemical,  or  thermal  work.  We  must 
inquire  into  this  electrical  energy,  and  into  the  rate 
at  which  it  is  generated  or  transformed. 

Power  is  the  rate  at  which  energy  is  being  received  or 
spent.  It  may  be  expressed  in  foot-pounds  per  second 
or  in  ergs  per  second.  James  Watt  considered  a  horse 
capable  on  the  average  of  working  at  the  rate  of  550  foot- 
pounds per  second  (against  gravity).  As  1  foot  =  30-48 
centimetres,  and  the  force  of  1  Ib.  (  =  453-6  grammes  x  981) 
=  445,000  dynes  nearly,  it  follows  that  1  horse-power  is 
worth  7,460,000,000  (or  746  x  107)  ergs  per  second. 

If  a  quantity  of  electricity  Q  is  moved  through  a 
difference  of  potential  V,  it  follows  from  the  definition 


442  ELECTRICITY   AND    MAGNETISM      PART  n 

(Art.  263)  that  the  work  done  is  equal  to  QV.  If  this 
is  occurring  in  a  battery  or  dynamo,  QVr  represents 
electrically  the  work  (chemical  or  mechanical)  done  on 
the  system,  or  the  energy  received  (electrically)  by  the 
system.  Now,  suppose  this  operation  to  have  occupied 
time  t,  the  rate  at  which  the  energy  is  being  imparted  to 
the  circuit  will  be  QV/t.  But  (Art.  162)  Q/*  =  C.  Hence 
the  power  given  to  the  circuit  is  equal  to  CV. 

This  justifies  the  statement  that  the  power  of  an  electric 
current  to  perform  useful  work,  whether  in  lighting, 
heating,  or  producing  mechanical  actions,  is  proportional 
both  to  -the  strength  of  the  current,  and  to  the  electromotive- 
force  ivliich  drives  it.  In  other  words,  power  is  pro- 
portional to  both  amperes  and  volts  jointly.  Similarly 
the  power  of  a  steam  engine  is  proportional  not  only  to 
the  quantity  of  steam  it  uses,  but  also  to  the  pressure  at 
which  the  steam  is  supplied.  The  electric  unit  of  power 
will  then  be  the  power  of  a  current  of  1  ampere  driven 
by  an  electric  pressure  of  1  volt.  This  unit  is  known 
as  1  volt-ampere,  or  1  watt. 

Since  1  volt  =  108  absolute  units  of  E.M.F.  (Art.  354) 
and  1  ampere  =  10"1  absolute  units  of  current  (Art.  354), 
it  follows  that  1  watt  =  1C7  absolute  units  of  power  (i.e. 
107  ergs  per  second).  But  1  horse-power  =  746  x  107 
ergs  per  second  (see  above).  Hence  1  H.P.  =  746  watts. 

One  thousand  watts  is  called  1  kilowatt.  The  kilowatt 
is  therefore  approximately  1;\  H.P. 

To  find  the  number  of  watts  of  power  supplied  by  any 
dynamo  or  battery,  multiply  the  number  of  amperes  of 
current  by  the  number  of  volts  at  which  the  current  is 
driven.  The  same  rule  serves  to  calculate  the  power 
electrically  delivered  to  any  motor,  lamp,  accumulator, 
or  other  means  of  spending  electric  energy. 
Horse-power  =  C  x  V  -=-  746. 

Example.  —  If  a  current  of  20  amperes  is  supplied  to  a  big 
arc-lamp  at  a  pressure  of  5(5  volts,  find  the  amount  of 
power  absorbed  therein.  Ans.  1120  ivatts  or  1£  H.P. 


CHAP,  vin         POWER   MEASUREMENTS  443 

436.  Intake   and  Output  of  Power.  —  At   any  gen- 
erator battery,  dynamo,  or   thermopile,  power   is  taken 
in  to  the  electric  circuit.     At  any  motor  or  lamp,  or  at 
any  part   in   the   circuit  where  chemical  work  (electro- 
plating, decomposing  gases,  or  charging  accumulators)  is 
being  done  or  at  any  place  where  heat  is  being  evolved, 
power  is   being  given   out  by  the  electric   circuit.     At 
every  place  where   energy  is   coming   in   to   the   circuit 
there  will  be  an  electromotive-force  in  the  same  direction 
as  the  current,  and  helping  to  drive  it.     At  every  part 
where  energy  is  being  given  out  by  the  circuit  there  will 
be   an  electromotive-force   in  a  direction  opposed  to  the 
current.*  The  word  output^  as  applied  to  dynamos,  etc., 
means   the  number   of    watts    or    kilowatts    which  the 
machine  supplies  or  can  supply.     For  example,  a  dynamo 
capable  of  supplying   300   am-  ^    __^ 

peres  "  at "  100  volts  (meaning 
with  an  available  E.M.F.  of  100 
volts)  is  said  to  have  an  output 
of  30  kilowatts. 

437.  Power-Measurement. 
—  To  measure  the  power  given 
electrically  to   any  part  ab  of 
a  circuit  by  an  unvarying  cur- 
rent, it  suffices  to  measure  the 
current    with    an    ampere-meter 

(Art.   221),   and  the  potentials   across  the  part  with   a 
voltmeter  (Arts.  220,  290),  the  latter  being  of  course  con- 

*  Consider  the  mechanical  analogue  of  transmission  of  power  from  one 
pulley  to  another  pulley  by  a  belt.  The  effort  in  the  driving  pulley  is 
in  the  same  direction  as  the  motion  of  the  belt.  The  effort  in  the  driven 
pulley  is  opposed  in  direction  to  the  motion.  (See  also  Art.  248.) 

This  fundamental  principle  accounts  for  the  back-electromotive-forces 
observed  in  motors,  and  in  accumulators  while  being  charged.  Because 
of  it  we  know  (Art.  166)  that  the  seat  of  the  main  electromotive-force  in  a 
voltaic  cell  is  at  the  surface  of  the  zinc,  and  that  (Art.  422)  bismuth  is 
therino-electrically  positive  to  antimony. 

t  The  word  output,  as  applied  to  central  station  work,  is  sometimes 
used  in  sense  of  total  outflow  of  amperes  irrespective  of  voltage. 


444 


ELECTRICITY   AND  MAGNETISM       PART  n 


nected  as  a  shunt  as  in  Fig.  228.  The  product  of  volts 
and  amperes  gives  the  watts.  Or  a  wattmeter  may  be 
used  as  below. 

438.  Wattmeters.  —  The  product  of  amperes  and 
volts  may  be  measured  directly  by  means  of  a  wattmeter. 
This  name  is  given  to  a  variety  of  electrodynamometer 
(Art.  394)  in  which  the  fixed  and  movable  coils  constitute 
two  separate  circuits,  one  being  a  thick  wire  of  low  resist- 
^  _  ance  to  carry  the  amperes,  the 

other  being,  or  including,  a 
thin  wire  of  high  resistance  (as 
in  voltmeters)  to  receive  a  cur- 
rent proportional  to  the  volts. 
The  latter  circuit  is  to  be  con- 
nected as  a  shunt  to  the  part 
ab  of  the  circuit  in  which 
the  supplied  power  is  to  be 
measured.  In  Fig.  229,  as  in 
Fig.  228,  the  part  ab  is  an  arc- 


Fig.  229. 


lamp.  The  auxiliary  resistance  r  is  introduced  into  the 
thin-  wire  circuit  of  the  instrument,  the  whole  current 
flowing  through  the  thick-wire  circuit. 

Wattmeters  are  made  both  on  the  pattern  of  Siemens's 
dynamometer  (Art.  395)  and  on  that  of  Kelvin's  balances 
(Art.  396). 

When  power-measurements  have  to  be  made  on 
alternate-current  circuits,  separate  instruments  must  not 
be  used,  as  in  Art.  437,  to  measure  volts  and  amperes. 
For,  owing  to  the  differences  of  phase  (Art.  472)  between 
voltage  and  current,  the  apparent  waits,  got  by  multi- 
plying the  separate  readings,  will  be  in  excess  of  the  true 
watts  as  measured  by  a  wattmeter. 

439.  Power  wasted  in  Heating.  —  If  a  current  C  is 
driven  through  a  resistance  R,  the  volts  needed  will  (by 
Ohm's  law)  be 


The  power  CV  so  expended  will  merely  heat  the  resistance. 


CHAP,  vin  DISTRIBUTION  OF  ELECTRIC  ENERGY  445 

Substitute  for  V  its  value  as  above,  and  we  have 
Watts  wasted  =  CV  =  C2R  =  V2/R. 

Or,  if  the  expenditure  goes  on  for  t  seconds,  the  amount 
of  energy  turned  into  heat  (joules)  will  be 

Energy  =  QV  =  CtV  =  C2R*. 

The  nett  power  of  a  dynamo  or  battery  is  always  less 
than  its  gross  power,  because  of  internal  resistance.  If  r 
be  the  internal  resistance,  and  E  the  whole  electromotive- 
force,  the  nett  or  available  volts  V  =  E  —  Cr.  The  gross 
power  will  be  EC  watts.  But  the  nett  power  will  be 
VC  =  EC  -  C2r.  Or,  the  available  watts  equal  the  total 
watts  generated,  less  the  watts  wasted  in  internal 
heating. 

To  prove  Joule's  law  of  heating  as  given  in  Art.  427,  it  may  be 
remembered  that  the  mechanical  equivalent  of  heat  is  42  million 
ergs  to  1  calorie  (Joule's  equivalent)  ,  or  W  =  JU,  where  W  is  the 
work  in  ergs,  U  the  heat  in  calories,  and  J  =  4'2  X  107.  Hence 
U  =  C2R£/J.  But  to  reduce  the  work  to  ergs  we  must  multiply 
by  W  ;  whence  U  =  CPRt  X  0'24. 


44O.  Distribution  of  Electric  Energy.  —  Electric  en- 
ergy is  now  distributed  on  a  large  scale  for  lighting, 
motive  power  and  heating.  Large  Central  Stations  or 
Power-houses  are  erected  at  convenient  spots,  with  steam- 
engines  or  turbines  (if  water-power  is  available)  to  drive 
generating  machinery  (dynamos  and  alternators).  From 
the  power-house  distributing  mains  of  copper  go  out,  con- 
sisting of  feeders  leading  into  the  network  of  conductors 
that  runs  from  house  to  house. 

Supply  systems  may  be  classified  according  to  whether 
they  operate  at  a  loio  voltage  (or  low  pressure),  i.e.  from 
100  volts  (or  under)  to  300  volts  ;  high  voltage,  i.e.  from 
300  to  3000  volts;  or  extra  high  voltage,  over  3000 
volts.  The  low-voltage  systems  generally  use  continuous 
currents,  the  high-voltage  systems  generally  (but  not 
necessarily)  use  alternate  currents,  and  transformers  (Art, 


446  ELECTRICITY  AND   MAGNETISM      PART  n 


480)    to   transform   to   low  pressure   at   the   consumers' 
houses. 

Example.  —  The  City  of  London  Electric  Lighting  Company 
generates  alternate  currents  at  a  little  over  2000  volts  at 
its  power-house  on  the  south  side  of  the  Thames,  and 
sends  these  currents  through  the  feeders  to  sub-stations 
in  the  city,  where  they  are  transformed  down  to  currents 
twenty  times  as  large  at  a  pressure  of  100  volts ;  at  which 
low  pressure  they  supply  the  network  of  mains  and  house 
branches,  which  are  laid  in  conduits  under  the  streets. 

Since  the  power  of  a  current  depends  on  the  voltage 
at  which  it  is  supplied,  the  unit  of  supply  recognized  in 
law  is  based  on  the  unit  of  power,  the  watt  (Art.  435), 
and  is  defined  as  1000  watts  supplied  for  one  hour  (i.e. 
1  kilowatt-hour)  or  its  equivalent.  The  maximum  price 
which  the  English  Board  of  Trade  permits  the  supply 
company  to  charge  the  consumer  for  1  unit  is  eightpence. 

441.  Conditions  of  Electric  Supply.  —  Electric  energy 
is  almost  always  supplied  under  one  of  two  standard  con- 
ditions, either  — 

(a)  at  Constant  Voltage,  or 
(6)    with  Constant  Current. 

In  the  former  case  the  circuit  is  branched,  and  the 
current  is  supplied  (usually  at  100  volts)  to  all  the  lamps 
or  motors  in  parallel  (Art.  409),  each  lamp,  etc.,  being 
independent  of  all  others;  and  the  current  varying  pre- 
cisely in  proportion  to  the  demand. 

In  the  latter  case,  seldom  used  except  for  strings  of 
arc-lamps,  the  circuit  is  undivided,  and  the  current 
(usually  10  amperes)  flows  through  all  the  lamps  in  series 
(Art.  168).  If  lamps  are  turned  out  (by  short-circuiting 
them)  the  voltage  must  be  reduced  to  keep  the  current 
constant. 

442.  Supply    Meters.  —  Meters  for  measuring    the 
supply  to  the  houses  of  consumers  are  of  several  kinds. 

(a)  Chemical  Meters.  —  The  current  or  a  known  fraction 


CHAP,  vin     ELECTRIC   SUPPLY   METERS  447 

of  it  is  passed  through  an  electrolytic  cell,  there  to 
deposit  copper  (Edison's  method)  or  dissolve  zinc 
(Jehl's  improved  Edison) .  The  amount  of  chemi- 
cal action  is  proportional  to  the  ampere-hours. 

(&)  Integrating  Meters.  —  A  uniformly -going  clock 
drives  a  counting  apparatus  through  an  inter- 
mediate gear  operated  by  the  current  (or  by  the 
watts),  such  intermediate  gear  being  such  that 
when  current  is  small  counting  is  small,  when 
current  large  counting  is  large.  An  integrating 
disk-and-roller,  or  an  integrating  cam,  is  a  usual 
mechanism,  its  operation  being  controlled  by  the 
motion  of  an  ampere-meter  or  wattmeter. 

(c)  Motor  Meters.  — 11  the  current  passes  through  the 
armature  of  a  small  motor  (Art.  443)  having  a 
constant  field,  having  its  speed  controlled  purely 
by  fluid  friction  (by  a  fan)  or  by  eddy-current 
friction  (in  a  copper  conductor  revolving  between 
magnet  poles,  Art.  457),  its  speed  will  at  every 
instant  be  proportional  to  the  current.  Hence 
such  a  motor  attached  to  a  suitable  counting-train 
of  wheels  will  serve  as  a  meter,  the  total  number 
of  revolutions  being  proportional  to  the  ampere- 
hours.  In  Perry's  meter  (1893)  the  revolving  part 
is  a  copper  bell  immersed  in  mercury,  revolving 
around  a  central  magnet  pole  (as  the  wire  does  in 
Fig.  201),  and  surrounded  by  an  external  S  pole 
with  ribbed  projections  to  promote  eddy-currents. 
In  Schallenberger's  meter  for  alternate  currents 
the  motor  drives  a  fan.  In  Elihu  Thomson's 
meter,  which  records  the  watt-hours,  the  revolving 
armature  is  of  fine  wire  and  high  resistance,  con- 
nected as  shunt,  while  the  fixed  coils  that  serve  as 
field-magnet  take  the  whole  current  supplied.  So 
the  torque  is  proportional  to  the  watts ;  while  a 
copper  disk  revolving  between  magnet  poles,  by 
its  drag  keeps  the  speed  proportional  to  the  torque. 


448  ELECTRICITY  AND   MAGNETISM      PAIIT  11 

(d)  Retarded  Clocks.  —  Current  may  be  made  to  act 
upon  the  rate  of  a  clock,  by  flowing  in  a  coil 
under  the  pendulum  bob  if  the  latter  is  a  magnet. 
Any  force  added  thus  to  gravity  or  subtracted 
from  it  will  cause  the  clock  to  gain  or  lose.  Ayr- 
ton  and  Perry  proposed  to  measure  the  supply 
by  the  total  time  gained  or  lost  by  a  clock.  In 
Aron's  meter,  of  which  this  is  the  principle,  there 
is  a  double  clock  with  two  pendulums,  only  one 
of  which  is  acted  on  by  the  current.  A  train  of 
counting  wheels  is  geared  to  record  the  difference 
between  the  two. 


LESSON    XXXVIII.  —  Electric    Motors    (Electromagnetic 
Engines) 

443.  Electric  Motors.  —  Electromagnetic  engines,  or 
motors,  are  machines  in  which  the  motive  power  is  de- 
rived from  electric  currents  by  means  of  their  electro- 
magnetic action.  In  1821  Faraday  showed  a  simple  case 
(Art.  393)  of  rotation  produced  between  a  magnet  and  a 
current  of  electricity.  Barlow  produced  rotation  in  a 
star-wheel,  and  Sturgeon  in  a  copper  disk,  when  traversed 
radially  by  a  current  while  placed  between  the  poles  of 
a  horse-shoe  magnet.  In  1831  Henry,  and  in  1833 
Ritchie,  constructed  small  engines  producing  rotation  by 
electromagnetic  means.  Fig.  230  shows  a  modification 
of  Ritchie's  motor.  An  electromagnet  DC  is  poised  upon 
a  vertical  axis  between  the  poles  of  a  fixed  magnet  (or 
electromagnet)  SN.  A  current,  generated  by  a  suitable 
battery,  is  carried  by  wires  which  terminate  in  two 
mercury-cups,  A,  B,  into  which  dip  the  ends  of  the  coil 
of  the  movable  electromagnet  CD.  When  a  current 
traverses  the  coil  of  CD  it  turns  so  as  to  set  itself  in  the 
line  between  the  poles  NS,  but  as  it  swings  round,  the 
wires  that  dip  into  the  mercury-cups  pass  from  one  cup 


CHAP.    VIII 


ELECTRIC   MOTORS 


449 


to  the  opposite,  so  that,  at  the  moment  when  C  approaches 
S,  the  current  in  CD  is  reversed,  and  C  is  repelled  from 
S  and  attracted  round  to  N,  the  current  through  CD 
being  thus  reversed  every  half  turn.  In  larger  motors 
the  mercury-cup  arrangement  is  replaced  by  a  commutaior 
(devised  by  Sturgeon),  consisting  of  a  copper  tube,  slit 
into  two  or  more  parts,  and 
touched  at  opposite  points  by 
a  pair  of  metallic  springs  or 
"  brushes." 

In  another  early  form  of 
motor,  devised  by  Froment, 
bars  of  iron  fixed  upon  the 
circumference  of  a  rotating 
cylinder  are  attracted  up  to- 
wards an  electromagnet,  in 
which  the  current  is  automati- 
cally broken  at  the  instant 
when  each  bar  has  come  close 
up  to  its  poles.  In  a  third 
kind,  an  electromagnet  is  made 
to  attract  a  piece  of  soft  iron 
alternately  up  and  down,  with 
a  motion  like  the  piston  of  a 
steam-engine,  which  is  con- 
verted by  a  crank  into  a  rotatory  motion.  In  these  cases 
the  difficulty  occurs  that,  as  the  attraction  of  an  electro- 
magnet falls  off  rapidly  at  a  distance  from  its  poles,  the 
attracting  force  can  only  produce  effective  motion  through 
very  small  range.  Page  from  1888  to  1850  designed 
various  motors,  in  some  of  which  iron  plungers  were 
sucked  into  hollow  tubular  coils  of  wire  in  which  currents 
were  caused  to  circulate  at  recurring  intervals. 

In  1839  Jacobi  propelled  a  boat  along  the  river  Neva 
at  the  rate  of  2\  rniles  per  hour  with  an  electromagnetic 
engine  of  about  one  horse-power,  worked  by  a  battery  of 
64  large  Grove's  cells. 
2  G 


450  ELECTRICITY    AND   MAGNETISM      PART  n 

Jacob!  appears  to  have  been  the  first  to  recognize, 
about  1850,  that  the  action  of  the  electric  motor  is  the 
simple  converse  of  that  of  the  dynamo  or  generator. 
Every  magneto-electric  generator  or  dynamo,  such  as  is 
used  in  electric  lighting,  can  also  work  as  a  motor,  giving 
out  mechanical  power  when  supplied  with  electric  currents 
from  some  other  source.  Indeed  the  dynamos  designed 
as  generators  make  far  more  efficient  motors  than  any 
of  the  older  sorts  of  electromagnetic  engines,  which  were 
little  more  than  toys. 

In  1882  an  iron  screw-boat  capable  of  carrying  12 
persons,  and  driven  by  two  such  motors,  with  a  power 
of  about  3  horse-power,  the  current  being  furnished 
by  45  accumulators,  was  worked  upon  the  Thames  at  a 
speed  of  8  miles  per  hour.  There  is  now  a  whole  flotilla 
of  electric  launches  on  the  Thames. 

444.  Modern  Electric  Motors.  —  These  are  of  two 
kinds:  (1)  those  for  use  with  continuous  currents;  (2) 
those  for  use  with  alternate  currents.  The  former  are 
constructed  precisely  on  the  plan  of  continuous  current 
dynamos  (Art.  462)  having  fixed  field  magnets  and  rotat- 
ing armature.  The  armature  is  dragged  round  by  the 
mutual  action  of  the  currents  flowing  in  the  copper 
conductors  and  the  magnetic  field  in  which  the  conductors 
lie.  As  explained  ii>  Art.  340,  the  force  acting  laterally 
on  the  conductors  is  proportional  to  the  product  of 
current  and  field.  Hence  if  very  powerful  field-magnets 
are  employed,  a  great  torque  (or  turning  moment)  can  be 
produced  without  requiring  too  great  a  current  to  be  sent 
into  the  armature.  The  two  factors  of  mechanical  rotatory 
power  are  torque  (  —  angular  force)  and  angular  speed.  If 
the  field  of  the  motor  is  maintained  constant  the  torque 
is  proportional  to  the  current  and  the  speed  is  proportional 
to  the  volts.  If  E  is  the  electromotive-force  generated 
(in  direction  opposing  the  current,  see  Art.  436)  in  the 
revolving  armature,  and  C  the  current  supplied  to  it,  the 
electrical  and  mechanical  expressions  for  the  power 


CHAP,  viii        EFFICIENCY  OF   MOTORS  451 

(watts)  imparted  to  the  armature  are 
CE  =  cmT, 

where  n  is  revolutions  per  second,  T  the  torque,  and  a  a 
coefficient  depending  on  the  units  chosen. 

If  the  armature  current  is  supplied  from  mains  at 
constant  voltage,  strengthening  the  magnetic  field  has 
the  effect  of  slowing  speed,  for  equal  power;  and  weak- 
ening the  field  quickens  the  speed.  Alternate-current 
motors  are  described  in  Arts.  484  to  486. 

445.  Efficiency  of  Motors.  —  If  an  ampere-meter  be 
included  in  the  circuit  with  a  battery  and  a  motor,  it 
is  found  that  the  current  is  weaker  when  the  motor  is 
working  than  when  the  motor  is  standing  still,  and  that 
the  faster  the  motor  runs  the  weaker  does  the  current 
become.  This  is  due  to  the  E.M.F.  generated  in  the 
revolving  armature  of  the  motor,  which  necessarily  (Art. 
436)  opposes  the  current.  If  the  motor  only  exerts  a 
small  back  electromotive- force  it  cannot  utilize  much  of 
the  power  of  the  current.  If  V  be  the  volts  at  which  the 
current  is  supplied,  and  E  the  counter-electromotive-force 
generated  by  the'  motor,  and  C  the  current,  then  VC  = 
gross  power  supplied,  EC  =  nett  power  utilized ;  and 
dividing  the  latter  by  former  we  get,  as  the  electrical 

V 

efficiency  of  the  motor,  the  ratio  — . 

Example.  —  Suppose  V  =  100  volts  and  E  =  90  volts,  the 
efficiency  will  be  90  per  cent. 

To  make  the  efficiency  as  high  as  possible  the  motor 
should  be  so  arranged  (either  by  strengthening  its  mag- 
netic field,  or  by  letting  it  run  faster)  that  E  is  very 
nearly  equal  to  V.  In  that  case  the  motor  will  utilize 
nearly  all  the  energy  that  flows  to  it.  But  since,  by 
Ohm's  law,  the  current  is  =  (V  —  E)/r,  where  r  is  the 
internal  resistance  of  the  motor,  it  follows  that  when  E 
becomes  nearly  equal  to  V  the  current  will  be  reduced  to 


452 


ELECTRICITY   AND   MAGNETISM      PART  n 


a  small  fraction  what  it  would  be  if  the  motor  were  at 
rest.  The  diagram  (Fig.  231)  makes  the  matter  plainer. 
Let  the  line  OV  represent  by  its  length  the  volts  of 
supply  V,  and  let  OE  represent  the  volts  generated  in 
the  armature,  proportional  to  speed  and  to  field.  On 
OV  describe  the  square  OVWX,  and 
V  K  W  draw  the  diagonal  and  the  lines  EH, 

KL.  Then  the  area  EVWH  is  pro- 
Hi  portional  to  the  gross  power,  being 
V(V  — E),  and  area  GLXH  is  propor- 
tional to  the  nett  power,  being 
E(V  — E).  These  two  areas  become 
more  nearly  equal,  though  both  be- 
come small,  when  E  is  increased  to 
be  nearly  equal  to  V.  The  area 


L     X 


Fig.  231. 


GLXH,  the  nett  output  of  the  motor,  is  a  maximum 
when  E  =  £V ;  but  then  the  efficiency  would  be  only  50 
per  cent. 

The  fact  that  when  E  is  small  the  current  is  enormous 
is  of  great  advantage  in  the  starting  of  motors ;  for  at 
starting  the  great  rush  of  current  (which  would  destroy 
them  if  it  lasted)  produces  a  great  torque,  and  the  motor 
soon  gets  up  speed  and  so  cuts  down  the  current  to  the 
working  amount. 

446.  Electric  Locomotion.  —  Motors  placed  on  cars 
or  on  separate  locomotives  can  propel  them  singly  or  in 
trains  provided  the  requisite  power  is  supplied.  This 
may  be  done  in  several  ways  :  — 

(a)  A  battery  of  charged  accumulators  is  carried  on 

the  car. 

(6)  Current  is  furnished  from  a  power-house,  at  some 
convenient  point,  to  the  rails  on  which  the  cars 
run,  and  which  act  as  outgoing  and  return 
conductors,  and  are  insulated.  The  cars  (which 
have  insulated  wheels)  pick  up  their  currents 
from  the  rails. 
(c)  Current  is  furnished  from  a  power-house,  to  a  third 


CHAP,  vni      TRANSMISSION   OF   POWER  453 

rail  insulated  from  earth.  From  this  the  current 
is  picked  up  by  the  car,  the  ordinary  rails  being 
used  as  return  conductor. 

(d)  Current  is  furnished  from  a  power-house  to  an 
overhead  line,  with  which  the  car  makes  contact 
as  it  runs  by  means  of  a  trolley-wheel  fixed  on  a 
long  rod  above  the  car. 

Method  (a)  is  not  economical,  owing  to  weight  of 
accumulators.  Plan  (6)  is  the  one  used  by  Siemens  in  the 
first  electric  tramway  put  down,  in  Berlin,  in  1879.  Plan 
(c)  is  used  in  several  heavy  electric  railroads  in  England, 
to  furnish  current  to  locomotives  of  200  to  400  horse- 
power. Plan  (d)  is  used  for  tramways  chiefly  in  the 
United  States,  where  there  are  now  (1894)  thousands  of 
miles  of  light  roads  so  equipped. 

447.  Electric  Transmission  of  Power.  —  Power  may 
be  transmitted  to  great  distances  electrically  from  a 
generator  at  one  end  of  the  circuit  to  a  motor  at  the  other. 
A  mountain  stream  may  be  made  to  turn  a  turbine  which 
drives  a  dynamo  or  alternator,  the  currents  from  which 
are  conveyed  to  some  centre  of  population  by  insulated 
wires  to  the  motor  which  reconverts  the  electrical  power 
into  mechanical  power.  Scores  of  such  examples  are  now 
at  work.  In  the  striking  demonstration  at  Frankfort,  in 
1891,  140  horse-power  was  conveyed  from  the  falls  of  the 
Neckar  at  Lauffen,  117  miles  away,  through  three  wires 
only  4  millimetres  in  diameter,  with  a  nett  efficiency  of 
74  per  cent,  including  all  losses. 

Fig.  232  illustrates  the  case  of  a  simple  transmission 
between  two  machines.  In  one  the  electromotive-force 
drives  the  current,  in  the  other  the  electromotive-force 
opposes  the  current.  The  first  acts  as  generator  (by  the 
principle  of  Art.  436),  the  second  as  motor.  If  their 
respective  electromotive-forces  are  Ej  and  E2  the  electrical 
efficiency  of  the  transmission  is  the  ratio  E2/Er 

The  power  lost  in  the  line  by  reason  of  its  resistance 
is  the  chiof  difficulty  to  face  in  such  transmissions,  owing 


454 


ELECTRICITY  AND    MAGNETISM      PART  n 


to  the  prohibitive  price  of  copper  for  carrying  large 
currents  without  overheating.  The  watts  wasted  in  a  line 
of  resistance  11  are  (Art.  439)  =  C2R.  The  gross  watts 
utilized  are  (Art.  435)  =  CVn?  where  VM  is  the  volts  at 
the  motor  end.  Hence  the  power  that  must  be  poured  in 
to  the  sending  end  of  the  line  C2R  +  CVM  watts.  Now 
it  will  be  obvious  that  one  may  keep  the  C2R  loss  constant 
and  yet  increase  the  power  that  is  transmitted  by  increas- 


GENERATOR 


MOTOR 


Fig.  232. 


ing  VM  the  voltage  at  the  motor  — using  in  fact  a  high- 
voltage  motor,  and  of  course  a  high-voltage  generator  to 
correspond.  To  put  the  matter  in  another  way.  Let 
VG  be  the  volts  at  the  generator  end  of  the  line, 
(VG  _  VM)R  will  be  =  C.  Now  we  may  keep  C  con- 
stant (and  therefore  the  C2R  loss  constant)  and  yet  in- 
crease the  voltages,  provided  VG  —  VM  remains  as 
before. 

Example.  —  Suppose  a  line  of  copper-wire  20  miles  long  has 
resistance  of  100  ohms.  A  current  of  6  amperes  in  it  will 
waste  3600  watts  or  nearly  5  horse-power.  To  send  0 
amperes  through  100  ohms  requires  a  difference  of 
potentials  of  GOO  volts.  Suppose  VG  =  1000  and 
VM  =  400,  VG  —  VM  =  600.  The  watts  sent  in  are 
CVG  =  6000,  and  the  watts  delivered  are  CVM  =  2400. 
Of  8  horse-power  put  in  only  about  84  are  delivered,  the 


CHAP,  viii  THE   ELECTRIC   AKC  455 


efficiency  being  VM/VQ  =  40  per  cent.  Now  suppose 
VG  increased  to  2000  volts,  and  VM  to  1400.  VG  —  VAT  = 
GOO,  as  before.  C  =  G  amperes,  as  before.  C'2R  loss  is 
oi.OO  watts,  as  before.  But  watts  sent  iu  are  now  12,000 
(over  16  H.P.),  and  the  watts  delivered  are  8400 
(III  H.P.).  Whilst  the  efficiency  is  now  70  per  cent. 

It  is  therefore  clear  that  high  voltage  is  the  secret  of 
success  in  the  electrical  transmission  of  energy,  whether 
for  lighting  or  power,  to  long  distances.  In  the  trans- 
mission of  energy  from  the  Falls  of  Tivoli  to  light  the 
city  of  Rome  sixteen  miles  away,  a  pressure  of  5000  volts 
is  successfully  used.  In  the  scheme  for  utilizing  the 
power  of  Niagara  Falls,  now  on  the  way,  a  voltage  of 
80,000  is  proposed. 


LESSON  XXXIX.  —  Electric  Light 

448.  The  Electric  Arc.  —  If  two  pointed  pieces  of 
carbon  are  joined  by  wires  to  the  terminals  of  a  powerful 
voltaic  battery  or  other  generator  of  electric  currents, 
and  are  brought  into  contact  for  a  moment  and  then 
drawn  apart  to  a  short  distance,  a  kind  of  electric  flame 
called  the  arc  or  "  voltaic  "  arc  is  produced  between  the 
points  of  carbon,  and  a  brilliant  light  is  emitted  by  the 
white  hot  points  of  the  carbon  electrodes.  This  phenome- 
non was  first  noticed  by  Humphry  Davy  in  1800,  and  its 
explanation  appears  to  be  the  following :  —  Before  con- 
tact the  difference  of  potential  between  the  points  is 
insufficient  to  permit  a  spark  to  leap  across  even  T^^7  of 
an  inch  of  air-space,  but  when  the  carbons  are  made  to 
touch,  a  current  is  established.  On  separating  the  carbons 
the  spark  at  parting  volatilizes  a  small  quantity  of  carbon 
between  the  points.  Carbon  vapour  being  a  partial  con- 
ductor allows  the  current  to  continue  to  flow  across  the 
gap,  provided  it  be  not  too  wide ;  but  as  the  carbon 
vapour  has  a  very  high  resistance  it  becomes  intensely 
heated  by  the  passage  of  the  current,  and  the  carbon  points 


456 


ELECTRICITY  AND  MAGNETISM 


also  grow  hot.  Since,  however,  solid  matter  is  a  better 
radiator  than  gaseous  matter,  the  carbon  points  emit  far 
more  light  than  the  arc  itself,  though  they  are  not  so  hot. 
The  temperature  of  the  arc  is  simply  determined  by  the 
temperature  at  which  carbon  volatilizes  ;  about  3500°  C. 
according  to  Violle.  In  the  arc  the  most  infusible  sub- 
stances, such  as  flint  and  diamond,  melt ;  and  metals  such 
as  gold  and  platinum  are  even  vaporized  readily  in  its 

intense  heat.  When  the 
arc  is  produced  in  the  air 
the  carbons  slowly  burn 
away  by  oxidization.  It  is 
observed,  also,  that  particles 
of  carbon  are  volatilized  off 
and  torn  away  from  the  -j- 
electrode,  which  becomes 
hollowed  out  to  a  cup-shape, 
or  crater,  and  if  the  gap  be- 
tween the  carbons  is  small 
some  of  these  particles  are 
deposited  on  the  —  elec- 
trode, which  assumes  a 
pointed  form,  as  shown  in 
Fig.  233.  The  resistance  of  the  arc  may  vary,  according 
to  circumstances,  from  0-2  ohm  upwards,  according  to  the 
length  and  section  of  the  flame.  The  arc  also  exerts  an 
opposing  electromotive-force  of  its  own,  amounting  to 
about  35  volts  when  continuous  currents  are  used,  and 
the  arc  is  silent.  When  it  becomes  unstable  and  hisses, 
the  back  electromotive-force  is  much  lower.  The  seat  of 
this  back  electromotive-force  is  at  the  surface  of  the  crater 
where  the  work  of  volatilizing  the  carbon  is  being  done. 

To  produce  an  electric  light  satisfactorily  a  minimum 
electromotive-force  of  40  to  50  volts  is  necessary  if  con- 
tinuous currents  are  used.  With  alternate  currents  30  to 
35  volts  suffice.  The  usual  current  for  arc  lamps  of  1000 
to  2000  candle  power  is  from  5  to  10  amperes.  With 


CHAP.    VIII 


ARC  LAMPS  457 


weaker  currents  or  smaller  electromotive-forces  it  is  im- 
practicable to  maintain  a  steady  arc.  For  search-lights 
on  board  ship  and  for  lighthouses,  arc  lights  of  greater 
power  are  produced  by  using  thicker  carbons  and  supply- 
ing them  with  currents  of  20  to  100  or  more  amperes. 
The  common  size  of  carbon  rod  in  use  is  10  or  11 
millimetres  in  diameter :  the  consumption  is  roughly  1 
inch  per  hour,  the  +  carbon  consuming  much  faster  than 
the  —  carbon.  The  internal  resistance  of  the  ordinary 
Daniell's  or  Leclanche's  cells  (as  used  in  telegraphy)  is 
too  great  to  render  them  serviceable  for  producing  arc 
lights.  A  battery  of  40  to  60  Grove's  cells  (Art.  182) 
is  efficient,  but  will  not  last  more  than  2  or  3  hours.  A 
dynamo-electric  machine  (such  as  described  in  Arts.  461 
to  469),  worked  by  a  steam-engine,  is  the  generator  of 
currents  in  practical  electric  lighting.  The  quantity  of 
light  emitted  by  an  arc  lamp  differs  in  different  directions, 
the  greatest  amount  being  emitted  (when  the  -f  carbon 
is  at  the  top)  at  an  angle  of  about  45°  downwards.  Most 
of  it  comes  from  the  white  hot  crater,  very  little  from  the 
negative  point.  In  the  alternate-current  arc  the  carbon 
points  are  alike  and  emit  equal  light.  The  current  must 
not  alternate  more  slowly  than  40  periods  per  second. 
The  total  quantity  of  light  emitted,  when  the  current  is 
supplied  at  a  fixed  voltage,  is  not  quite  proportional  to 
the  current,  but  increases  in  a  somewhat  higher  ratio. 
Doubling  the  current  makes  rather  more  than  twice  as 
much  light. 

449.  Arc  Lamps.  —  Davy  employed  wood  charcoal 
for  electrodes  to  obtain  the  arc  light.  Pencils  of  hard 
gas-carbon  were  later  introduced  by  Foucault.  In  all  the 
more  recent  arc  lamps,  pencils  of  a  more  dense  and  homo- 
geneous artificial  coke-carbon  are  used.  These  consume 
away  more  regularly,  and  less  rapidly,  but  still  some 
automatic  contrivance  is  necessary  to  push  the  points  of 
the  carbons  forward  as  fast  as  needed.  The  mechanism 
of  the  arc  lamp  should  "  strike  "  the  arc  by  causing  the 


458 


ELECTRICITY   AND   MAGNETISM 


pencils  to  touch,  and  then  separate  them  to  the  requisite 
distance,  about  5  millimetres ;  the  mechanism  should  also 
"  feed  "  the  carbons  into  the  arc  as  fast  as  they  are  con- 
sumed, and  it  should  also  cause 
the  points  to  approach  or  re- 
cede automatically  in  case  the 
arc  becomes  too  long  or  too 
short ;  it  should  further  bring 
the  carbons  together  for  an 
instant  to  strike  the  arc  again 
if  by  any  chance  the  flame  goes 
out.  Arc  Lamps  or  "regula- 
tors," fulfilling  these  condi- 
tions, have  been  invented  by  a 
number  of  persons.  The  earli- 
est was  invented  in  1847  by 
W.  E.  Staite.  Arc  lamps  may 
be  classified  as  follows  :  — 

(a)  Clockwork  Lamps.  — 
Fig.  234  shows  the  regulator 
of  Foucault  as  constructed  by 
Duboscq;  in  this  lamp  the 
carbon-holders  are  propelled 
by  a  train  of  clockwork  wheels 
actuated  by  a  spring.  An 
electromagnet  at  the  base, 

VJlBlP  through    which     the    current 

Iff  <^-»   I     '?.-.  runs,  attracts  an  armature  and 

governs  the  clockwork.  If  the 
current  is  too  strong  the  arma- 
ture is  drawn  down,  and  the 
clockwork  draws  the  carbons 
farther  apart.  If  the  current 
is  weakened  by  the  increase  of  the  resistance  of  the  arc  as 
the  carbons  burn  away,  the  armature  is  drawn  upwards 
by  a  spring,  and  a  second  train  of  wheels  comes  into  play 
and  moves  the  carbons  nearer  together.  Clockwork  arc 


Fig.  284 


CHAP.    VIII 


ARC   LAMP   MECHANISM 


459 


lamps  have  also  been  devised  in  which  the  weight  of  the 
carbon-holders  drive  the  clockwork  mechanism.  Of  this 
class  was  Serrin's  lamp,  which  from  1855  to  the  present 
time  has  been  largely  used  for  lighthouses,  and  for  the 
optical  lantern. 

(6)  Brake-wheel  Lamps.  —  Another  mechanism  for  reg- 
ulating the  rate  of  feeding  the  carbon  into  the  arc  consists 
in  the  addition  of  a  brake-wheel ; 
the  brake  which  stops  the  wheel 
being  actuated  by  an  electro- 
magnet which  allows  the  wheel 
to  run  forward  a  little  when  the 
resistance  of  the  arc  increases 
beyond  its  normal  amount.  In 
Fig.  235  B  is  the  brake-wheel, 
L  the  lever  which  governs  it,  C 
an  iron  core  of  the  coil  S  inserted 
in  the  circuit.  When  current  is 
switched  on,  the  core  is  drawn 
up,  causing  L  to  grip  B  and  turn 
it  a  little,  so  parting  the  carbons 
and  striking  the  arc. 

(c)  Solenoid  Lamps.  —  In  this 
class  of  arc  lamp  one  of  the  car- 
bons   is    attached    to    an    iron 
plunger  capable  of  sliding  verti- 
cally up  or  down  inside  a  hollow 
coil    or    solenoid,   which,    being 
traversed   by  the   current,  regu- 
lates the  position  of  the  carbons  and  the  length  of  the 
arc.     Siemens  employed  two  solenoids  acting  against  one 
another  differentially,  one  being  a  main-circuit  coil,  the 
other  being  a  fine-wire  coil  connected  as  a  shunt  to  the 
arc.     The  shunt  coil  acts  as  a  voltmeter  to  watch  the  arc 
and  feed  the  carbons  forward  when  the  volts  rise  above 
the  normal,  it  being  set  to  control  the  feeding  mechanism. 

(d)  Clutch  Lamps.  —  A  somewhat   simpler  device  is 


Fig.  235. 


460  ELECTRICITY  AND   MAGNETISM     PAHT   n 

that  of  employing  a  clutch  to  pick  up  the  upper  carbon- 
holder,  the  lower  carbon  remaining  fixed.  In  this  kind 
of  lamp  the  clutch  is  worked  by  an  electromagnet,  through 
which  the  main  current  passes.  If  the  lamp  goes  out  the 
magnet  releases  the  clutch,  and  the  upper  carbon  falls  by 
its  own  weight  and  touches  the  lower  carbon.  Instantly 
the  current  starts  round  the  electromagnet,  which  causes 
the  clutch  to  grip  the  carbon-holder,  and  raise  it  to  the 
requisite  distance.  Should  the  arc  grow  too  long,  the 
lessening  attraction  on  the  clutch  automatically  permits 
the  carbon-holder  to  advance  a  little. 

(e}  Motor  Lamps.  —  Sometimes  little  electric  motors 
are  used  to  operate  the  carbons  automatically. 

450.  Grouping  of  Arc  Lamps.  — If  the  condition  of 
supply  is  constant  voltage  the  arc  lamps  must  be  set  in 
parallel;  if  the  arc  lamps  are  to  be  run  in  series,  the 
same  current  flowing  in  succession  through  each  of  the 
lamps,  then  the  supply  must  be  of  a  current  of  unvarying 
strength.  In  this  case  a  shunt  circuit  is  neces- 
sary in  each  lamp. 

451.  Electric  Candles. —  To   obviate   the 
expense  and  complication  of  such  regulators, 
electric  candles  have  been  suggested.    Fig.  237 
depicts  Jablochkoff*  s  candle,  consisting  of  two 
parallel  pencils  of  hard  carbon  separated  by 
a  thin  layer  of  plaster  of  Paris  and  supported 
in  an  upright  holder.    The  arc  plays  across  the 
summit  between  the  two  carbon  wicks.     In 
order  that  both  carbons  may  consume  at  equal 
rates,  alternating  currents  must  be  employed. 

452.  Incandescent  Lamps  or  Glow-Lamps. 
—  Arc  lamps  of  an  illuminating  power  of  less 
than  100  candles  are  very  unsteady  and  un- 

'°'  '  economical.  For  small  lights  it  is  both  simpler 
and  cheaper  to  employ  a  thin  continuous  wire  or  filament 
of  some  infusible  conductor,  heated  to  whiteness  by 
passing  a  current  through  it.  Thin  wires  of  platinum 


CHAP,  vin  GLOW-LAMPS  461 

have  repeatedly  been  suggested  for  this  purpose,  but 
they  cannot  be  kept  from  risk  of  fusing.  Iridium  wires 
and  thin  strips  of  carbon  have  also  been  suggested 
by  many  inventors.  Edison  in  1878  devised  a  lamp 
consisting  of  a  platinum  spiral  combined  with  a  short- 
circuiting  switch  to  divert  the  current  from  the  lamp 
in  case  it  became  overheated.  Swan  in  February  1879 
publicly  showed  a  carbon  wire  lamp  in  a  vacuous  bulb. 
Edison  in  October  1879  devised  a  vacuum  lamp  with  a 
coiled  filament  made  of  lamp  black  and  tar  carbonized. 
Swan  in  January  1880  prepared  filaments  from  cotton 
thread  parchmentized  in  sulphuric  acid,  and  afterwards 
carbonized.  Edison  in  1880  substituted  a  flat  strip  of 
carbonized  bamboo  for  a  filament.  Lane  Fox  in  1879 
used  prepared  and  carbonized  vegetable  fibres.  Crookes 
used  a  filament  prepared  from  silk  or  vegetable  matter 
parchmentized  with  cuprammonic  chloride. 

Modern  glow-lamps  mostly  have  thin  carbon  wires 
prepared  from  parchmentized  cellulose,  which  is  then 
carbonized  in  a  closed  vessel.  Sometimes  the  filaments 
are  "  flashed  "  over  with  surface  carbon  by  being  moment- 
arily heated  electrically  in  a  carbonaceous  atmosphere. 
They  are  mounted  upon  platinum  supports  in  a  glass 
bulb  through  which  the  platinum  wires  pass  out,  and 
into  which  they  are  sealed,  the  bulbs  being  afterwards 
exhausted  of  air  and  other  gases,  the  vacuum  being  made 
very  perfect  by  the  employment  of  special  mercurial 
air-pumps.  The  bulbs  should  be  heated  during  exhaus- 
tion to  drive  out  residual  gases.  Carbon  is  the  only 
suitable  material  for  the  conductor  because  of  its  superior 
infusibility  and  higher  resistance.  It  also  has  the 
remarkable  property,  the  reverse  of  that  observed  in 
metals,  of  offering  a  lower  resistance  when  hot  than 
when  cold.  Two  common  forms  of  glow-lamp  are 
shown  in  Fig.  237 ;  the  typical  form  used  by  Swan  in 
England,  and  the  typical  form  perfected  by  Edison  in 
America.  The  resistance  of  such  lamps  varies  accord- 


462 


ELECTRICITY   AND    MAGNETISM      PART  n 


ing  to  size  and  length  of  the  filament.  A  modern  16 
candle-power  lamp  for  use  on  a  100-volt  circuit  will 
take  about  0-6  ampere.  That  is  to  say,  its  resistance 
when  hot  will  be  about  166  ohms  (or  over  200  ohms  when 
cold),  and  it  will  absorb  about 
60  watts.  This  is  at  the  rate 
of  less  than  4  watts  per  candle. 
Used  so,  it  will  last  on  the 
average  over  1000  hours  of 
burning.  Lamps  are  made  to 
give  equal  light  and  use  less 
current,  by  using  a  thinner  and 
rather  shorter  filament;  but 
then  they  do  not  last  so  long. 
The  surface  disintegrates  in 
time  if  forced  to  emit  too  much  light.  The  power  required 
to  operate  12  such  60-watt  lamps  will  be  720  watts,  or 
nearly  1  horse-power. 

The  following  table  gives  some  data  about  a  10-candle 
50- volt  lamp  if  used  at  different  voltages. 


Fig.  237. 


Volts. 

Amperes. 

Watts. 

Candle- 
power. 

Watts  per 
candle. 

Probable 
life  (hours). 

48 

0-77 

37 

8 

4'3 

3200 

50 

0-81 

40-5 

10 

4-05 

1500 

53 

0-87 

46-4 

14-5 

3-2 

800 

55 

0-92 

50-6 

18-5 

2-7 

480 

58 

0-99 

57-5 

25'5 

2-2 

250 

61 

1-06 

64-7 

35-5 

1-8 

150 

The  light  increases  as  about  the  sixth  power  of  the 
volts ;  the  energy  consumed  is  only  as  the  second  power. 
But  raising  the  volts  a  little  shortens  the  life  enormously. 

For  special  lamps  of  larger  candle-power,  up  to  800  or 
1000,  thin  filaments  cannot  be  used.  In  these  flat  strips 
or  thick  wires  of  carbon  are  used ;  they  give  out,  for  equal 
expenditure  of  power,  much  less  light  than  an  arc  lamp. 


CHAP,  viii  THREE- WIRE   SYSTEM  463 

453.  Grouping  of  Glow-Lamps.  —  Glow-lamps  are 
usually  grouped  in  parallel  (Fig.  238)  between  mains 
kept  at  constant  voltage.  A  common  value  for  the 
difference  of  potential 

between   the  +  and  —      — i -i j— j 1 ^    " 

mains  is  100  volts.  The      jA     |6    jA    |A    jA 

current   in  the   mains         I         I       II       I 

subdivides    and    flows 
through  each  lamp  in- 
dependently.    When  any  lamp  is  switched  on  it  does  not 
diminish  the  current  in   the  others,  but  by  opening  an 
additional  path  simply  causes  proportionately  more  current 
to  flow  from   the    source   of    supply.     The   method    of 
grouping  in  series  (Art.  168)  is  seldom  used  for  glow- 
lamps  ;  each  lamp  then  requires  an  automatic  cut-out  to 
prevent  the  rest  of  the  row  from  being  extinguished  in 
case  one  lamp  goes  out. 

Three-wire  systems,  in  which  a  third  or  neutral  wire  is 
introduced  between  the  +  and  the  —  main,  have  been 

devised      to     enable 

:±£-, -    . j +       higher  voltages  to  be 

1111         1  used,      and     thereby 

1  IT T enable  twice  as  many 

lamps  to  be  lit  with 

little    additional    ex- 

—        ^ ,  J — LJ L_     penditure  in  copper* 

Fio.  239  To  render  the  lamps 

on    one   side    of   the 

circuit  (Fig.  230)  independent  of  those  on  the  other, 
in  case  an  equal  number  do  not  happen  to  be  switched 
on  at  the  same  time,  the  middle  wire  (which  only  need 
be  thick  enough  to  carry  a  current  equal  to  the  difference 
between  the  currents  in  the  two  outer  wires)  is  carried 
back  to  the  station  and  kept  at  mean  potential  between  the 
two  outer  wires  by  the  use  of  two  dynamos  instead  of  one. 


CHAPTER  IX 

INDUCTANCE 

LESSON  XL.  —  Mutual  Induction 

454.  Mutual  Induction.  —  Mutual  induction  between 
two  circuits,  a  primary  and  a  secondary,  was  briefly 
considered  in  Art.  224.  Let  us  now  consider  the  electro- 
motive-forces so  induced.  Suppose  the  primary  coil  to 
have  Sx  spirals,  and  the  secondary  coil  S2  spirals.  At 
first  let  them  be  so  arranged  (by  use  of  an  iron  core  or 
by  geometric  juxtaposition)  so  that  all  the  magnetic  lines 
evoked  by  the  primary  coil  pass  through  all  the  spirals  of 
the  secondary  coil ;  both  coils  being  placed  close  together 
upon  a  suitable  core  of  laminated  iron. 

By  Art.  377  the  magnetic  flux  due  to  current  C  in 
the  primary  coil  will  be 

N  =  47TCS/J10Z, 

where  Z  is  the  reluctance  (Art.  376)  of  the  magnetic 
circuit.  The  total  amount  of  cutting  magnetic  lines  by 
the  S2  spirals  of  the  secondary,  when  current  C  is  turned 
off  or  on,  will  be 

S2N  =  47rCS1S2/10Z. 

Hence  it  follows  that  the  amount  of  cutting  of  mag- 
netic lines  (i.e.  the  induction  in  the  secondary  circuit) 
due  to  turning  on  or  off  10  amperes  (—1  C.G.8.  unit  of 
current)  in  the  primary,  will  be  47rS1S2/Z.     This  quantity 
464 


CHAP,  ix  MUTUAL   INDUCTION  465 

is  denoted  for  brevity  by  the  symbol  M.  If  the  primary 
and  secondary  coils  are  not  so  arranged  that  all  the  mag- 
netic lines  due  to  the  one  pass  through  the  spirals  of  the 
other,  then  M  will  have  a  less  value  than  47rS1S2/M. 

The  practical  unit  for  coefficients  of  mutual  induction 
is  the  same  as  for  those  of  self-induction,  namely  the 
henry  (Art.  354),  and  is  109  C.G.S.  units.  Hence  to 
bring  M  to  henries  we  must  divide  the  above  value  by  109. 

If  the  current  in  the  primary  is  varying  at  the  rate 
dC/dt,  the  electromotive-force  E2  thereby  induced  in  the 
secondary  circuit  will  be 

E=  -M-dC/dt, 

where  E  will  be  in  volts  if  M  is  expressed  in  henries,  C 
in  amperes,  and  t  in  seconds. 

The  value  of  M  for  the  small  induction  coils  used 
in  telephone  work  is  usually  about  0-01  henry ;  for  a 
Ruhmkorff  coil  capable  of  giving  a  spark  10  centimetres 
long  it  may  be  as  much  as  5  henries. 

Example.  —  Suppose  in  a  spark-coil  the  value  of  M  is  8  hen- 
ries, and  the  primary  current  changes  by  an  amount  of 
1  ampere  in  one  ten-thousandth  of  a  second  (owing  to 
the  quick-acting  break) ,  the  electromotive-force  induced 
in  the  secondary  during  that  ten-thousandth  of  a  second 
will  be  80,000  volts. 

To  measure  a  coefficient  of  mutual  induction,  there  are 
several  methods,  some  of  which  depend  on  the  use  of  Wheat- 
stone's  bridge ;  but  the  best  method  is  one  due  to  Carey 
Foster.  In  this  the  quantity  of  electricity  discharged 
from  a  condenser  of  known  capacity  K  shunted  by  a  re- 
sistance p  in  the  primary  circuit  is  balanced  against  the 
quantity  discharged  in  the  secondary  circuit  by  regulating 
a  resistance  q  in  the  latter.  Then  M  =  1\.pq. 

455.  Induced  Currents  of  Higher  Orders.  —  Joseph 
Henry,  an  independent  discoverer  of  magneto-electric 
induction,  discovered  that  the  variations  in  the  strength 
2n 


466  ELECTRICITY  AND   MAGNETISM      PART  n 

of  the  secondary  current  could  induce  tertiary  currents 
in  a  third  closed  circuit,  and  that  variations  in  the  ter- 
tiary currents  might  induce  currents  of  a  fourth  order, 
and  so  on.  A  single  sudden  primary  current  produces 
two  secondary  currents  (one  inverse  and  one  direct),  each 
of  these  produces  two  tertiary  currents,  or  four  tertiary 
currents  in  all.  But  with  alternating  or  periodic  there 
are  the  same  number  of  secondary  and  tertiary  fluctua- 
tions as  of  primary;  but  the  currents  of  the  second, 
fourth,  etc.  orders  will  be  inverse  in  the  direction  of  their 
flow  to  those  of  the  first,  third,  fifth,  etc. 

456.  Lenz's  Law.  —  In  Art.  223  it  was  explained 
how  an  increase  in  the  number  of  magnetic  lines  through 
a  circuit  (as  by  pushing  in  a  magnet)  tended  to  set  up  an 
inverse  current,  or  one  flowing  in  such  a  direction  as  is 
opposed  to  the  magnetism.  Similarly  a  decrease  in  the 
magnetic  lines  (as  by  withdrawing  the  magnet)  tends  to 
set  up  currents  that  will  pull  the  magnet  back.  Again, 
in  Art.  379,  it  was  laid  down  that  a  circuit  traversed  by 
a  current  experiences  a  force  tending  to  move  it  so  as  to 
include  the  greatest  possible  number  of  magnetic  lines-of- 
force  in  the  embrace  of  the  circuit.  But  if  the  num- 
ber of  lines  be  increased,  during  the  increase  there 
will  be  an  opposing  (or  negative)  electromotive-force  set 
up,  which  will  tend  to  stop  the  original  current,  and 
therefore  tend  to  stop  the  motion.  If  there  be  no  cur- 
rent to  begin  with,  the  motion  will  generate  one,  which 
being  in  a  negative  direction,  will  tend  to  diminish  the 
number  of  lines  passing  through  the  circuit,  and  so  stop 
the  motion.  Lenz,  in  1834,  summed  up  the  matter  by 
saying  that  in  all  cases  of  electromagnetic  induction  the  in- 
duced currents  have  such  a  direction  that  their  reaction  tends 
to  stop  the  motion  which  produces  them.  This  is  known  as 
Lenz's  law :  it  is  a  particular  case  of  the  more  general 
law  applicable  to  all  electromagnetic  systems,  namely, 
that  every  action  on  such  a  system,  ivhich,  in  producing  a 
change  in  its  configuration  or  state,  involves  a  transforma- 


CHAP,  ix  EDDY-CURRENTS  467 

tion  of  energy,  sets  up  reactions  tending  fo  preserve  unchanged 
the  configuration  or  state  of  that  system.  (Compare  Arts. 
204  and  379.) 

457.  Eddy-Currents  Induced  in  Masses  of  Metal.  — 
In  1824  Gambey  found  that  a  compass-needle  oscillating 
in  its  box  came  to  rest  sooner  if  the  bottom  of  the 
box  were  made  of  metal  than  if  of  wood.  Arago  in- 
vestigated the  matter,  and  found  a  copper  plate  under 
the  needle  most  effective  in  damping  its  motions.  He 
then  rotated  a  copper  disk  in  its  own  plane  underneath  a 
compass-needle,  and  found  that  the  needle  was  dragged 
round  as  by  some  invisible  friction.  A  copper  disk  sus- 
pended over  a  rotating  magnet  was  found  to  be  dragged 
by  it.  Attempts  were  made  to  account  for  these  pheno- 
mena—  known  as  Arago' s  rotations  —  by  supposing  there 
to  be  a  sort  of  magnetism  of  rotation,  until  Faraday 
proved  them  to  be  due  to  induction.  A  magnet  moved 
near  a  solid  mass  or  plate  of  metal  induces  in  it  currents, 
which,  in  flowing  through  it  from  one  point  to  another, 
have  their  energy  eventually  frittered  down  into  heat, 
and  which,  while  they  last,  produce  (in  accordance  with 
Lenz's  law)  electromagnetic  forces  tending  to  stop  the 
motion.  These  currents,  circulating  wholly  within  the 
metal,  are  called  eddy-currents.  If  a  cube  or  ball  of 
good  conducting  metal  be  set 
spinning  between  the  poles  of 
such  an  electromagnet  as  Fig. 
182,  and  the  current  be  sud- 
denly turned  on,  the  spinning 
metal  stops  suddenly.  In  a 
copper  disk  revolving  between 
the  poles  of  a  magnet  (Fig.  240)  Fig.  240. 

there  is  a  pair  of  eddies  in  the 

part  passing  between  the  poles,  and  these  currents  tend  to 
pull  the  disk  back.  In  fact,  any  conductor  moved  forcibly 
across  the  lines  of  a  magnetic  field  experiences  a.jnechani- 
cal  resistance  due  to  the  induced  currents  which  oppose 


468  ELECTRICITY   AND   MAGNETISM      PART  n 

its  motion.  Foucault  showed  *  that  if,  by  sheer  force,  a 
disk  be  kept  spinning  between  the  poles  of  a  powerful 
electromagnet  it  will  become  hot  in  consequence  of  the 
eddy-currents  induced  in  it. 

The  eddy-current  drag  on  a  moving  conductor  (some- 
times called  the  magnetic  friction)  is  a  force  proportional 
to  the  speed  and  proportional  to  the  square  of  the  mag- 
netic field ;  for  the  force  (Art.  340)  is  proportional  to  the 
product  of  field  and  current,  and  the  current  (circulating 
round  a  given  path)  is  proportional  both  to  field  and  to 
speed.  Hence  eddy-current  drag  is  employed  in  some 
forms  of  electric  supply  meter  (Art.  442)  to  control  the 
speed  of  the  moving  part. 

Alternating  electric  currents  also  set  up  eddy-currents 
in  masses  of  metal  near  them ;  for  this  reason  the  iron 
cores  of  transformers  (Art.  480)  and  of  dynamo  arma- 
tures (Art.  463)  must  be  carefully  laminated,  otherwise 
there  will  be  heating  and  waste  of  energy. 

Further,  eddy-currents  in  any  mass  of  metal  between 
a  primary  and  a  secondary  circuit  will  tend  to  set  up 
in  the  secondary  tertiary  electromotive-forces  opposing 
those  set  up  by  the  primary.  Hence  interposed  sheets  of 
metal  act  as  induction-screens. 


LESSON  XLI.  —  Self-induction 

458.  Self-induction.  —  It  has  been  pointed  out  in 
Art.  224  how  when  a  current  in  a  circuit  is  increasing  or 
diminishing,  it  exercises  an  inductive  effect  upon  any 
neighbouring  circuit ;  this  inductive  effect  being  due  to 
the  change  in  the  magnetic  field  surrounding  the  varying 
current.  But  since  the  magnetic  lines  surrounding  a 
current  may,  as  they  move  inwards  or  outwards  from  the 
wire,  cut  across  other  parts  of  the  same  circuit,  it  is  evident 

*  Hence  some  writers  call  the  eddy-currents  "Foucault's  currents," 
though  they  were  known  years  before  Foucault's  experiments  were  made. 


CHAP,  ix  SELF-INDUCTION  469 

that  a  current  may  act  inductively  on  itself.  The  self- 
inductive  action  is  great  if  the  circuit  consists  of  a  coil  of 
many  turns,  and  is  still  greater  if  the  coil  possesses  an 
iron  core.  Suppose  a  coil  of  wire  to  possess  S  spirals,  and 
that  it  generates  a  magnetic  flux  through  these  spirals  of 
N  lines  when  current  C  is  turned  on.  Then  it  is  clear 
that  turning  on  the  current  will  have  the  same  effect  as  if 
a  magnet  of  N  lines  were  suddenly  plunged  into  the  coil ; 
and  turning  off  the  current  will  have  the  same  effect  as  if 
the  magnet  were  suddenly  withdrawn.  Now  (Art.  225) 
the  current  induced  by  plunging  a  magnet  into  a  coil  is 
an  inverse  current  tending  to  push  it  out,  while  that 
induced  by  withdrawing  the  magnet  is  a  direct  current, 
tending  to  attract  it  back.  It  follows  that  the  self- 
induced  electromotive-force  on  turning  the  current  on  will 
tend  to  oppose  the  current,  and  prevent  it  growing  as 
quickly  as  it  otherwise  would  do,  while  that  induced  on 
stopping  the  current  will  tend  to  help  the  current  to 
continue  flowing.  In  both  cases  the  effects  of  self- 
induction  is  to  oppose  change :  it  acts  as  an  electro- 
magnetic inertia. 

In  the  case  supposed  above,  where  the  coil  has  S  turns, 
the  total  cutting  of  magnetic  lines  in  the  operation  will 
=  S  x  N,  provided  all  the  lines  thread  through  all  the 
spirals.  Let  the  symbol  L  be  used  to  represent  the  total 
amount  of  cutting  of  lines  by  the  circuit  when  a  current 
of  1  ampere  is  suddenly  turned  on  or  off  in  it.  Clearly 
L  x  C  =  S  x  N.  This  quantity  L  is  called  "  the  induct- 
ance "  of  the  circuit.  It  was  formerly  called  "the 
coefficient  of  self-induction  "  of  the  circuit.  The  unit  of 
induction  is  called  the  henry,  and  corresponds  to  a 
cutting  of  108  magnetic  lines  when  1  ampere  is  turned  on 
or  off. 

Since  (in  circuits  without  iron  cores)  N  is  proportional 
to  S,  it  follows  that  L  is  proportional  to  S2.  Or  since 
(see  Art.  377)  N  =  47rCS/10Z,  and  the  total  cutting  of 
lines  by  the  S  spirals  (if  all  the  lines  pass  through  all  the 


470  ELECTRICITY   AND   MAGNETISM      PART  n 

spirals)  is  S  x  N,  hence  the  induction  when  10  amperes 
are  turned  on  or  off  will  be 

L  =  47rS2/Z, 

which  may  be  expressed  in  henries  by  dividing  by  109. 
If  all  the  lines  do  not  pass  through  all  the  spirals  the 
value  of  L  will  be  less  than  this. 

The  self-induced  electromotive-force  will  depend  upon 
the  rate  at  which  the  current  is  changing  ;  for  if  the  total 
cutting  SN  take  place  in  time  t,  it  follows  (Art.  225) 
that :  — 

E  =  -  SN/«  =  -  LC/t. 

But  since  the  rate  at  which  the  current  changes  is  not 
uniform,  E  is  also  not  uniform.  If  in  an  element  of  time 
dt  the  current  charges  by  an  amount  c/C,  the  rate  of  charge 
of  the  current  is  dC/dt,  and  the  self-induced  electromotive- 
force  is  =  —  IfdC/dt. 

The  formal  definition  of  the  henry  (Art.  354)  is  based 
on  the  above  expression  in  order  that  it  may  apply  to 
circuits  with  iron  cores  as  well  as  to  circuits  without 
them. 

The  energy  of  the  magnetic  field  surrounding  the 
current  is  equal  to  |LC2,  since  while  the  field  is  growing 
up  to  have  LC  lines  in  total,  the  average  value  of  the 
current  is  |C. 

To  measure  a  coefficient  of  self-induction  there  are 
several  methods :  — 

(a)  Alternate- Current  Method.  —  The  volts  V  required 
to  send  current  C  at  frequency  n  through  coil  having 
resistance  R  and  coefficient  of  self-induction  L  are 
V  =  C  \/R2  +  47r2n2L2 ;  or,  if  the  resistance  is  negligible, 
V  =  2irnCL,  whence  L  =  V/27rnC  (see  Art.  472). 

(ft)  Bridge  Methods.  —  Of  several  bridge  methods  the 
best  is  Maxwell's.  Let  balance  be  obtained  in  usual 
way ;  key  in  battery  circuit  being  put  down  before  key 
in  galvanometer  circuit  (Art.  415).  Then  press  the  keys  in 


CHAP,  ix     EFFECTS   OF   SELF-INDUCTION  471 

reverse  order,  when  the  presence  of  self-induction  in  one 
of  the  four  arms  will  upset  balance,  the  needle  giving  a 
kick  a  proportional  to  the  self-induction.  Now  introduce 
in  the  same  arm  an  additional  small  resistance  r,  such 
that  when  keys  are  again  operated  in  the  usual  order 
there  is  a  small  permanent  deflexion  8.  If  the  periodic 
time  of  swing  of  the  needle  be  T  the  following  formula 
then  holds  :  —  L  =  Tra/2ir8. 

(c)  Secohmmeter  Method.  —  Ayrton  and  Perry  invented 
an  instrument  which  alternately  makes  and  breaks  the 
battery  circuit  of  the  bridge  and  only  allows  the  galvan- 
ometer to  be  in  operation  during  a  short  interval  of  time 
T  immediately  after  each  making  of  the  battery  circuit 
(the  galvanometer  at  other  times  being  short-circuited). 
As  the  current  is  increasing  during  this  interval,  the 
self-induction  L  of  a  coil  placed  in  one  of  the  arms  of  the 
bridge  acts  as  though  there  were  an  additional  resistance 
r  in  that  arm.  The  formula  is  then,  L  =  Tr.  As  L  is 
then  the  product  of  seconds  and  ohms,  Ayrton  and  Perry 
proposed  for  the  unit  (now  called  the  henry)  the  name 
of  secohm. 

459.  Effects  of  Inductance.  —  The  presence  of  in- 
ductance in  a  circuit  affects  the  currents  in  several  ways. 
The  special  choking-effect  on  alternate  currents  is  dealt 
with  in  Art.  474.  The  effects  on  battery  currents  are 
also  important.  So  long  as  the  current  is  not  changing 
in  strength  inductance  has  no  effect  whatever ;  but  while 
the  current  is  starting  or  while  it  is  dying  away  the 
presence  of  inductance  greatly  affects  it.  In  all  cases 
inductance  tends  to  oppose  any  change  in  the  strength  of 
the  current;  as  may  be  foreseen  from  Lenz's  law  (Art. 
456).  When  a  current  is  increasing  in  strength  induct- 
ance causes  it  to  increase  more  slowly.  When  a  current 
is  dying  away  inductance  tends  to  prolong  it. 

The  existence  of  inductance  in  a  circuit  is  attested  by 
the  so-called  extra-current,  which  makes  its  appearance 
as  a  bright  spark  at  the  moment  of  breaking  circuit.  If 


472  ELECTRICITY  AND   MAGNETISM      PART  n 

the  circuit  be  a  simple  one,  and  consist  of  a  straight  wire 
and  a  parallel  return  wire,  there  will  be  little  or  no 
inductance ;  but  if  the  circuit  be  coiled  up,  especially  if 
it  be  coiled  round  an  iron  core,  as  in  an  electromagnet, 
then  on  breaking  circuit  there  will  be  a  brilliant  spark, 
and  a  person  holding  the  two  ends  of  the  wires  between 
which  the  circuit  is  broken  may  receive  a  shock,  owing  to 
the  high  electromotive-force  of  this  self-induced  extra 
current.  This  spark  represents  the  energy  of  the  mag- 
netic field  surrounding  the  wire  suddenly  returning  back 
into  the  circuit.  The  extra-current  on  "  making  "  circuit 
is  an  inverse  current,  and  gives  no  spark,  but  it  prevents 
the  battery  current  from  rising  at  once  to  its  full  value. 
The  extra-current  on  breaking  circuit  is  a  direct  current, 
and  therefore  keeps  up  the  strength  of  the  current  just 
at  the  moment  when  it  is  about  to  cease.  To  avoid  the 
perturbing  effects  of  inductance,  resistance-coils  are 
always  coiled  back  upon  themselves  (Art.  414). 

Even  when  a  circuit  consists  of  two  parallel  straight 
wires  there  is  a  magnetic  field  set  up  between  them, 
giving  inductive  reactions.  The  coefficient  of  self-induc- 
tion for  two  wires  of  length  /  and  radius  a  at  an  axial 
distance  b  apart  in  air  is 


where  L  is  in  henries;  a,  b  and  I  in  centimetres,  and  /i 
the  permeability  of  the  wire. 

46O.  Helmholtz's  Equation.  Time-constant.  —  From 
that  which  precedes  it  is  clear  that  whenever  a  current 
is  turned  on  there  is  a  variable  period  while  the  current 
is  growing  up  to  the  value  which  it  will  reach  when 
steady,  namely  the  value  as  determined  by  Ohm's  law. 
But  during  the  variable  period  Ohm's  law  is  no  longer 
applicable. 

Von  Helmholtz,  who  investigated  mathematically  the 
effect  of  self-induction  upon  the  strength  of  a  current, 


CHAP,  ix  GROWTH  OF  CURRENT  473 

deduced  the  following  important  equations  to  express  the 
relation  between  the  inductance  of  a  circuit  and  the  time 
required  to  establish  the  current  at  full  strength  :  — 

Let  dt  represent  a  very  short  interval  of  time,  and  let 
the  current  increase  during  that  short  interval  from  C  to 
C  +  dC.  The  actual  increase  during  the  interval  is  dC, 
and  the  rate  of  increase  in  strength  is  dC/dt.  Hence,  if 
the  inductance  be  L,  the  electromotive-force  of  self-induc- 
tion will  be  —  LdC/dt,  and,  if  the  whole  resistance  of  the 
circuit  be  R,  the  strength  of  the  opposing  extra-current 

will  be  —  -  •  —  during  the  short  interval  dt  ;  and  hence 
R     dt 

the  actual  strength  of  current  flowing  in  the  circuit  during 
that  short  interval  instead  of  being  (as  by  Ohm's  law  it 
would  be  if  the  current  were  steady)  C  =  E/R,  will  be 


R     R     dt 

To  find  out  the  value  to  which  the  current  will  have 
grown  after  a  time  t  made  up  of  a  number  of  such  small 
intervals  added  together,  requires  an  application  of  the 
integral  calculus,  which  at  once  gives  the  following 
result  :  — 


(where  c  is  the  base  of  the  natural  logarithms). 

Put  into  words,  this  expression  amounts  to  saying  that 
after  a  lapse  of  t  seconds  the  self-induction  in  a  circuit  on 
making  contact  has  the  effect  of  diminishing  the  strength  oj 
the  current  by  a  quantity,  the  logarithm  of  whose  reciprocal  is 
inversely  proportional  to  the  inductance,  and  directly  propor- 
tional to  the  resistance  of  the  circuit  and  to  the  time  that  has 
elapsed  since  making  circuit. 

The  quantity  L/R,  the  reciprocal  of  which  appears 
in  the  exponential  expression,  is  known  as  "  the  time-con- 
stant "  or  "  persistence  "  of  the  circuit.  It  is  the  time 


474 


ELECTRICITY   AND   MAGNETISM      PART  n 


required  by  the  current  to  rise  to  a  certain  fraction,  namely 
(e  -l)/e,—  or  0-034  —  of  its  final  value. 

A  very  brief  consideration  will  show  that  in  those 
cases  where  the  circuit  is  so  arranged  that  the  inductance 
L  is  small  as  compared  with  the  resistance  R,  so  that  the 

time-constant  is  small,  the  term  f  e          ]  will  vanish  from 

the  equation  for  all  appreciable  values  of  L 

On  the  other  hand  if  L  is  great  compared  with  R,  the 
current  during  its  growth  will  be  governed  almost  entirely 
by  the  inductance,  and  not  by  the  resistance  of  the 
circuit,  which  will  act  as  though  its  resistance  were 


These  matters  are  graphically  depicted  in  Fig.  241,  in  which 
there  are  two  curves  of  rise  of  current.  Consider  a  circuit  having 
E  =  10  volts,  R  =  1  ohm,  L  =  10  henries.  The  steady  current  will 

be  10  amperes  ;  but  at  the  end 
of  1  second,  as  may  be  calculated 
by  Helmholtz's  equation,  the 
current  is  only  0'95  of  an  am- 
pere !  In  2  seconds  it  is  T81  , 
in  5  seconds  3'95,  in  10  seconds 
6'M  amperes  (see  curve  A)  .  At 
the  end  of  a  whole  minute  it  is 
only  9-975  amperes.  Suppose 
now  we  increase  the  resistance 
to  2  ohms,  and  reduce  the  in- 
ductance to  5  henries.  The 
final  value  of  the  current  will 


0     2     4     6      8     10    12    14    16    IS  2O 

Fig.  241. 


be  only  5  amperes  instead  of  10  ; 

but  it  will  rise  more  quickly  than  before  (see  curve  B).  At  the 
end  of  1  second  it  will  be  lg(547  ampere,  in  2  seconds  2'755,  in  10 
seconds  4-91  amperes.  We  conclude  that  for  all  apparatus  that 
is  required  to  be  rapid-acting  (relays,  telephones,  chronographs, 
etc.),  it  is  much  more  important  to  keep  down  the  inductance 
than  the  resistance  of  the  circuit.  We  also  see  that  the  rule  (Art. 
407)  so  often  given,  about  making  the  resistance  of  a  battery 
equal  to  that  of  the  rest  of  the  circuit,  is  quite  wrong  for  cases 
of  rapid  action.  If  the  circuit  has  self-induction  as  well  as 
resistance  then  it  is  better  to  group  the  cells  of  the  battery  so 
as  to  have  higher  resistance,  namely  put  them  all  in  series. 


CHAP,  ix  EXTRA-CURRENT  475 

In  fact  everything  goes  on  as  though  at  time  t  after 
"  make "  there  were  two  currents  flowing  in  opposite 
directions  at  once  ;  one  the  ordinary  current  flowing  from 
the  first  at  full  strength,  the  other  the  extra-current 

"p1     — Rt/L 

having  the  value  —  -^  e         ;  the  actual  current  being  the 
R 

difference  between  the  two. 

At  "  break  "  of  circuit  everything  goes  on  as  if,  the 
ordinary  current  having  dropped  suddenly  to  zero,  there 
was  superposed  an  extra-current  having  the  value 

+  —€         ;  but  here,  since  there  is  introduced  into  the 
R 

circuit  a  resistance  of  unknown  amount  (the  resistance 
along  a  spark  being  indefinite),  the  calculation  becomes 
impracticable.  We  know  that  R  is  very  great ;  hence 
we  know  that  the  variation  will  be  more  sudden,  and 
that  the  self-induced  E.M.F.  at  "  break"  is  much  greater 
than  that  at  "  make."  The  self-induced  E.M.F.  would 
be  represented  by  the  expression  Et  —  Ee  -R«/L.  This 
expression  should  be  compared  with  that  for  the  E.M.F. 
of  discharge  of  a  condenser  of  capacity  K  through  a 
resistance  R  (see  also  Art.  326),  which  is  Vt  =  V0e~'/KR. 
From  this  it  appears  that  in  the  case  of  a  condenser  dis- 
charge KR  acts  as  the  time-constant  L/R  does  in  the 
case  of  self-induction. 

The  actual  quantity  of  electricity  conveyed  by  the 
"  extra-current "  is  equal  to  that  which  would  be  con- 
veyed by  current  of  strength  E/R  of  lasting  for  time 
L/R;  or  =  EL/R2.  At  the  "make"  of  the  circuit  the 
retardation  causes  the  flow  of  electricity  to  be  lessened 
by  the  amount  q  =  EL/R2.  The  energy  which  is  stored 
up  outside  the  wire  while  the  current  grows  up  from  0  to 
its  final  value  C  is  equal  to  ^E  =  |LC2. 


CHAPTER  X 

DYNAMOS    AND    TRANSFORMERS 

LESSON    XLII.  —  Magneto-electric    and     Dynamo-electric 
Generators 


461.      Simple    Magneto-electric    Machines.  —  Fara- 
day's  discovery  of  the   induction  of    currents  in  wires 

by  moving  them  across  a 
magnetic  field  suggested  the 
construction  of  magneto- 
electric  machines  to  generate 
currents  in  place  of  voltaic 
batteries,  and  Faraday  him- 
self constructed  the  first  of 
such  machines  (Fig.  132)  in 
242  1831.  In  the  early  attempts 

of  Pixii  (1833),  Saxton, 
and  Clarke,  bobbins  of  insulated  wire  were  fixed  to  an 
axis  and  spun  rapidly  in  front  of  the  poles  of  strong  steel 
magnets.  But,  since  the  currents  thus  generated  were 
alternately  inverse  and  direct  currents,  a  commutator 
(which  rotated  with  the  coils)  was  fixed  to  the  axis  to 
turn  the  successive  currents  all  into  the  same  direction. 
Fig.  242  illustrates  the  plan  adopted  by  Sturgeon  in 
1836,  using  a  split  tube  of  copper  to  commute  the  con- 
nexion to  the  outer  circuit  at  each  half  turn.  In  the 
figure  the  wire  coil  is  supposed  to  be  spun  around  a  longi- 
476 


CHAP,  x    MAGNETO-ELECTRIC   MACHINES 


477 


tudinal   axis;    the   upper  portion   coming    towards   the 
observer.     The  arrows  show  the  direction  of  the  induced 
currents     delivered     by     the 
commutator  to  the    contact- 
springs  or  brushes.     The  little 
magneto  -  electric     machines, 
still  sold  by  opticians,  are  on  _^ 
this  principle.      Holmes  and 
Van     Malderen     constructed 
more  powerful  machines,  the 
latter  combining  around  one 
axis  sixty-four  separate  coils  rotating  between  the  poles 
of  forty  powerful  magnets. 

In  1856  Werner  Siemens  devised  an  improved  arma- 
ture, in  which  the  coils  of  wire  were  wound  shuttle-wise 
upon  a  grooved  iron  core,  which  concentrated  the  mag- 
netic lines  in  a  powerful  field  between  the  poles  of  a  series 
of  adjacent  steel  magnets.  The 
next  improvement,  due  to  Wilde, 
was  the  employment  of  electro- 
magnets instead  of  steel  magnets 
for  producing  the  field  in  which 
the  armature  revolved ;  these 
electro-magnets  being  excited  by 
currents  furnished  by  a  small 
auxiliary  magneto-electric  '  ma- 
chine, also  kept  in  rotation.  If 
instead  of  commuting  the  cur- 
rents the  ends  of  the  revolving 
coil  are  connected  to  a  pair  of  contact  rings,  on  each  of 
which  presses  a  brush,  the  machine  will  deliver  alternate 
currents.  Fig.  243  illustrates  a  primitive  form  of  alter- 
nator. It  will  be  seen  that  if  the  induced  E.M.F.  in  the 
wires  as  they  move  past  the  N  pole  towards  the  observer 
is  from  left  to  right,  the  two  contact  rings  will  alternately 
become  -f  and  —  at  each  half  turn. 

462.    Dynamo-electric  Machines.  —  The  name  dynamo- 


Flg.  244. 


478  ELECTRICITY   AND   MAGNETISM      PART  n 

electric  machine,  or,  briefly,  dynamo,  is  given  to  any 
machine  for  converting  mechanical  power  into  electrical 
power  by  the  operation  of  producing  relative  motion 
between  magnets  and  conductors.  The  part  which  acts 
as  magnet  is  termed  the  field-magnet.  In  continuous-cur- 
rent generators  it  usually  stands  still ;  in  some  alternators 
it  is  made  to  revolve.  Its  function  is  to  provide  a  large 
number  of  magnetic  lines.  The  part  which  acts  as  the 
active  conductor,  cutting  the  magnetic  lines  and  having 
electromotive-force  induced  in  it  is  termed  the  armature. 
In  continuous-current  generators,  the  armature  revolves 
between  the  poles  of  the  field-magnet.  In  some  alterna- 
tors it  is  stationary.  In  the  early  machines  the  magnet- 
ism of  the  field  magnets  was  independently  excited. 
Various  suggestions  were  made  by  Hjorth,  Murray,  S.  A. 
Varley,  and  others  to  use  the  currents  generated  in  the 
armature  to  excite  the  field-magnets.  This  was  done  in 
1867  by  Varley,  Werner  Siemens,  and  Wheatstone ;  the 
small  current  induced  by  the  feeble  residual  magnetism 
being  sent  around  the  electromagnet  to  exalt  its  magnet- 
ism, and  prepare  it  to  induce  still  stronger  currents.  To 
machines  so  rendered  self-exciting  Werner  Siemens  gave 
the  distinguishing  name  of  dynamo-electric  machines  or 
generators,  to  distinguish  them  from  the  generators  in 
which  permanent  steel  magnets  are  employed.  In  either 
case  the  current  is  due  to  magneto-electric  induction  ;  and 
in  either  case  also  the  energy  of  the  currents  so  induced 
is  derived  from  the  dynamical  power  of  the  steam-engine 
or  other  motor  which  performs  the  work  of  moving  the 
rotating  coils  of  wire  in  the  magnetic  field.  But  the 
name  has  been  extended  to  all  generators,  whether  self- 
exciting  or  not.  In  all  of  them  the  electromotive-force 
generated  is  proportional  to  the  number  of  turns  of  wire 
in  the  rotating  armature,  and  to  the  speed  of  revolution. 
When  currents  of  small  electromotive-force,  but  of  con- 
siderable strength  are  required,  as  for  electroplating,  the 
rotating  armatures  of  a  generator  must  be  made  with 


DYNAMOS  479 


small  internal  resistance,  and  therefore  of  a  few  turns  of 
stout  wire  or  ribbon  of  sheet  copper.  For  producing 
currents  at  a  high  electromotive-force  the  armature  must 
consist  of  many  turns  of  wire  or  of  rods  of  copper  suitably 
connected,  and  it  must  revolve  in  a  very  powerful  mag- 
netic field. 

463.  Continuous-current  Dynamos.  —  The  dynamos 
of  different  makers  differ  in  the  design  of  their  field- 
rnagnets  and  in  the  means  adopted  for  securing  conti- 
nuity in  the  induced  currents.  Most  continuous-current 
dynamos  have  a  simple  field-magnet  with  two  poles  : 
but  many  large  machines  are  made  with  four,  six,  or  eight 
poles.  But  the  modern  armature  is  complex.  A  simple 
coil,  such  as  Fig.  242,  with  its  2-part  commutator  will  not 
yield  a  steady  current ;  for  twice  in  each  revolution  the 
E.M.F.  dies  away  to  zero.  The  coils  must  be  grouped  so 
that  some  of  them  are  always  active.  In  most  dynamos 
the  armature  winding  is  constructed  as  a  closed  coil, 
the  wire  being  wound  on  a  ring  core  of  iron  (Pacinotti's 
core  with  teeth,  Gramme's  core  without  teeth),  or  as  a 
drum  over  a  cylindrical  core  (Siemens's  or  Von  Hefner's 
plan),  or  having  the  coils  arranged  flat  as  a  disk 
(Desrozier's  plan).  In  all  these  cases  the  convolutions  are 
joined  up  so  that  (like  the  ring  winding  in  Fig.  190)  the 
coil  is  endless.  If  the  current  is  brought  in  at  one  side 
of  such  a  coil  and  taken  out  at  the  other  side  there  will 
be  two  paths  through  the  coil.  As  the  coil  spins  between 
the  poles  of  the  magnet  the  electromotive-forces  induced 
in  the  ascending  and  descending  parts  will  tend  to  send 
the  currents  in  parallel  through  these  parts;  and  con- 
sequently contact-brushes  must  be  set  to  take  off  the 
currents  from  the  revolving  coils  at  the  proper  places. 
The  brushes  are,  however,  set  in  contact  not  with  the 
coils  themselves  but  with  a  commutator,  Fig.  244,  consist- 
ing of  a  number  of  copper  bars,  insulated  from  one 
another,  and  joined  on  to  the  armature  coil  at  regular 
intervals.  Consider,  for  example,  a  Gramme  ring  made 


480  ELECTRICITY   AND   MAGNETISM      PART  n 

as  it  were  of  a  number  of  bobbins  wound  upon  a  ring 
core  of  iron  wire.  Each  bobbin  constitutes  one  section  of 
the  winding,  and  they  are  all  joined  together,  the  end  of 
one  section  to  the  beginning  of  the  next,  and  each  such 
junction  is  joined  down  to  a  bar  of  the  commutator. 
The  current  cannot  pass  from  one  bar  of  the  commutator 
to  the  next  without  traversing  the  intervening  section  of 


Fig.  246. 

the  windings.  The  commutator  revolves  with  the  arma- 
ture ;  while  the  brushes,  which  are  clamped  in  suitable 
holders,  press  against  its  surface,  and  are  set  in  such  a 
position  that  the  current  passes  into  them  with  as  little 
sparking  as  possible.  It  is  found  that  to  prevent  spark- 
ing the  brushes  must  be  set  a  little  in  advance  of  the 
diameter  that  is  symmetrical  between  the  poles  :  for  the 
current  in  each  section  of  the  winding  is  reversed  as  it 
passes  under  the  brush,  and  for  sparkless  reversal  needs  to 


CHAP,  x  DYNAMO   CALCULATIONS  481 

be  moving  at  that  instant  in  a  magnetic  field  of  sufficient 
strength.  The  current  in  the  armature  exercises  a  mag- 
netizing action,  and  tends  to  distort  the  magnetic  field  in 
the  direction  of  the  rotation.  To  prevent  serious  distor- 
tion and  sparking,  the  field-magnet  is  made  very  powerful 
and  massive.  The  "brushes"  that  receive  the  current 
were  originally  bunches  of  springy  wires :  in  modern 
machines  they  are  built  up  of  copper  strip  or  copper 
gauze,  or  consist  of  small  blocks  of  carbon.  Fig.  245  de- 
picts a  modern  type  of  dynamo,  having  a  vertical  magnet 
of  massive  wrought  iron  magnetized  by  currents  flowing 
in  coils  wound  upon  the  two  limbs.  Below,  between  the 
polar  surfaces  which  are  bored  out  to  receive  it,  is  the 
revolving  armature  (in  this  case  a  drum-arrnature)  with 
the  commutator  and  brushes.  The  core  of  the  armature 
is  built  up  of  thin  iron  disks  lightly  insulated  from  one 
another,  to  prevent  eddy-currents. 

All  continuous-current  dynamos  will  run  as  motors 
(Art.  443),  if  supplied  with  current  at  the  proper 
voltage. 

For  fuller  descriptions  of  dynamos,  and  technical  details  of 
construction,  the  reader  is  referred  to  the  author's  treatise  on 
Dynamo-electric  Machinery. 

464.  Dynamo  Calculations. — In  a  2-pole  dynamo 
if  N  be  the  total  number  of  magnetic  lines  sent  by  the 
field-magnet  through  the  armature,  S  the  number  of  wires 
or  conductors  in  series  on  the  armature,  counted  all 
round,  and  n  the  number  of  revolutions  per  second,  the 
electromotive-force  generated  by  the  spinning  armature 
will  be 

E  =  nSN/108, 

for  the  cutting  per  second  of  magnetic  lines  is  proportional 
to  each  of  these  three  quantities,  and  we  divide  by  108  to 
bring  to  volts.  As  with  batteries  (Art.  171),  so  with 
dynamos,  if  there  is  an  internal  resistance  r,  the  available 
2i 


482  ELECTRICITY  AND   MAGNETISM      PART  n 

volts  at  the  terminals  V  will  be  less  than  the  whole  volts 
generated  by  an  amount  equal  to  rC,  the  lost  volts. 

V  =  E  -  rC. 

As  the  electrical  efficiency  of  the  machine  is  the  ratio 
V/E,  it  is  evident  that  r  should  be  as  low  as  possible. 

Example.— A  dynamo  having  N  =  7,170,000,  S  =  120,  running 
at  780  revs,  per  min.  (=  13  revs,  per  sec.)  will  generate 
an  electromotive-force  of  111  volts.  If  r  =  0'033  ohm, 
then  when  C  =  210  amperes,  ?'C  =  7  volts.  Hence  V  =  104 
volts. 

The  current  C  which  a  dynamo  yields  depends  on  the 
resistance,  etc.,  of  the  circuit  it  supplies.  The  maximum 
current  it  can  supply  is  limited  by  several  considerations, 
such  as  the  heating  of  its  parts,  the  sparking  at  the 
brushes,  which  becomes  serious  if  too  much  current  is 
drawn  from  the  machine,  the  mechanical  strength  of  its 
parts,  and  also  the  power  of  the  driving-engine. 

The  gross  output  of  a  dynamo  is  the  number  of 
amperes  multiplied  by  the  total  electromotive-force  gene- 
rated, or  CE.  The  nelt  output  is  the  number  of  amperes 
multiplied  by  the  volts  at  terminals,  or  CV.  These  num- 
bers are  turned  to  horse-power  by  dividing  by  746. 

The  commercial  efficiency  of  a  dynamo  is  the  ratio 
between  the  nett  output  and  the  mechanical  power  ap- 
plied to  drive  the  machine. 

All  the  armature  conductors  of  a  dynamo  are  subject, 
when  the  machine  is  running,  to  a  mechanical  drag  op- 
posing the  rotation.  This  is  due  to  the  action  between 
the  magnetic  field  and  the  current  (Art.  340). 

A  little  power  is  wasted  by  eddy-currents  (Art.  457), 
and  by  hysteresis  (Art.  368)  in  the  armature  core,  and 
also  a  little  by  eddy-currents  (Art.  463)  in  the  moving 
masses  of  metal,  so  diminishing  the  efficiency:  but  in 
well-constructed  machines  such  losses  are  slight. 

To  calculate  the  field-magnet  windings  the  formulae  of 


CHAP,  x      WINDING  OF   FIELD-MAGNETS 


483 


Arts.  377  and  399  must  be  applied  (see  exercise  21  on 
Chap.  V.)- 

465.  Excitation  of  Field-Magnets. — There  are  sev- 
eral modes  of  exciting  the  magnetism  of  the  field-mag- 
nets, giving  rise  to  the  following  classification  :  — 

1.  Magneto  Machine,  with  permanent  steel  magnets. 

2.  Separately-excited  Dynamo;  one  in  which  the  cur- 
rents used  to  excite  the  field-magnets  are  furnished  by  a 
separate  machine  called  an  "  exciter." 

3.  Separate-coil  Dynamo,  with  a  separate  coil  wound 
on  the  armature  to  generate  the  exciting  current. 

4.  Series-Dynamo,  wherein  the  coils  of  the  field-mag- 
net are  in  series  with  those  of  the  armature  and  the 


Fig.  246. 


Fig.  247. 


Fig.  248. 


external  circuit  (Fig.  246),  and  consist  of  a  few  turns  of 
thick  wire. 

5.  Shunt-Dynamo,   in   which  the   coils  of   the  field- 
magnet  form  a  shunt  to  the  main  circuit;    and,    being 
made  of  many  turns  of  thin  wire,  draw  off  only  a  small 
fraction  of  the  whole  current  (Fig.  247). 

6.  Compound-Dynamo,  partly  excited  by  shunt  coils, 
partly  by  series  coils  (Fig.  248). 

The  last  three  modes  are  illustrated  in  the  accompany- 
ing diagrams.  Each  variety  of  winding  has  certain 
advantages  depending  on  conditions  of  use. 


484 


ELECTRICITY   AND   MAGNETISM       PART  n 


466.  Characteristic  Curves.  —  To  study  the  behav- 
iour of  various  types  of  dynamo,  Hopkinson  devised 
the  method  of  characteristic  curves,  wherein  the  two  ele- 
ments of  output  —  the  volts  and  the  amperes  —  are  plotted 
out.  If  a  series-dynamo  is  examined  with  amperemeter 
and  voltmeter,  while  run  at  constant  speed  on  various 
loads,  its  performance  will  be  found  to  give  a  curve  like 
OQV  in  Fig.  249,  where  the  external  volts  are  plotted 

vertically,  the  amperes  hori- 
zontally. This  curve  is  the 
external  characteristic.  The 
volts  rise  as  the  current  is 
increased,  because  of  the 
increase  of  magnetization, 
but  when  this  is  near  satura- 
tion they  fall  again  because 
of  internal  resistance  and 
sundry  reactions.  At  any 
point  such  as  Q  the  resist- 
ance of  the  external  circuit 


Fig.  249. 


is  represented  by  the  slope  of  the  line  QO  (i.e.  by  the  trig- 
onometrical tangent  of  the  angle  QOX),  since  tan  QOX 
is  equal  to  QM/OM  (  —  the  volts  divided  by  the  amperes). 
If  line  OJ  be  drawn  so  that  tan  JOX  is  equal  to  the 
internal  resistance,  then  MN  will  represent  the  lost  volts 
when  the  current  =  OM.  Adding  to  QM  a  piece  PQ  = 
MN,  we  obtain  PM  as  the  corresponding  value  of  the 
total  electromotive-force.  In  this  way,  from  the  curve 
OV  we  can  construct  the  total  characteristic  OE.  It  will 
be  evident  that  if  the  total  resistance  (i.e.  the  slope  of  the 
line  OP)  be  increased  P  will  come  down  the  curve  toward 
O,  and  there  will  be  a  certain  point  at  which  any  further 
increase  in  the  slope  will  produce  a  sudden  drop  of  volts 
and  amperes  to  almost  zero.  This  is  a  peculiarity  of  series- 
machines;  when  running  at  a  given  speed  they  cease  to 
yield  any  current  if  the  resistance  exceeds  a  certain  criti- 
cal value,  depending  in  each  machine  on  its  construction. 


CHAP.    X 


CHARACTERISTIC   CURVES 


485 


For  a  shunt-dynamo  the  characteristic  has  a  different 
form.  When  the  machine  is  on  open  circuit,  giving  no 
current  externally,  the  shunt  circuit  is  fully  at  work 
exciting  the  magnet.  The  curve  YV  of  volts  at  ter- 
minals begins  at  a  high 
value,  and  as  the  current  is 
increased  by  diminishing 
the  resistance,  the  voltage 
gently  falls.  Part  of  this 
drop  is  due  to  internal  resist- 
ance ;  part  is  due  to  arma- 
ture reactions  and  magnetic 
distortion ;  and  part  to  the 
reduction  of  the  shunt 
current.  If,  as  before,  we 
draw  OJ  to  represent  by  its 


M 


Fig.  250. 


slope  the  internal  resistance,  we  can  find  the  lost  volts  MN 
and  add  these  on  above  Q,  so  obtaining  P,  a  point  on  the 
total  electromotive-force  curve.  This  also  drops  slightly. 
If  a  shunt-dynamo  be  short-circuited,  its  magnetism  is  at 
once  reduced  to  almost  zero.  To  regulate  the  voltage  of 
a  shunt-dynamo  a  suitable  rheostat  (Fig.  206)  may  be 
introduced  into  its  shunt  circuit,  to  vary  the  exciting 
current. 

467.  Constant  Voltage  Machines.  —  For  glow-lamp 
lighting,  machines  are  needed  that  will  maintain  the 
voltage  constant,  whether  the  current  going  to  the  mains 
be  small  or  large.  The  current  that  flows  out  of  the 
machine  will  regulate  itself  exactly  in  proportion  to  the 
demand ;  more  flowing  when  more  lamps  are  turned  on, 
provided  the  potential  difference  between  the  mains  is 
kept  constant.  For  this  purpose  neither  a  series-dynamo 
nor  a  shunt-dynamo  (driven  at  a  constant  speed)  will 
suffice;  though  by  hand-regulation,  as  above,  a  shunt- 
dynamo  may  be  used.  It  will  be  noted  that,  while  in 
shunt-machines  the  characteristic  drops  as  the  current 
is  increased,  in  series-machines  the  curve  rises.  Conse- 


486  ELECTRICITY   AND   MAGNETISM      PART  n 

quently,  by  using  a  compound-winding,  consisting  of  a 
shunt-winding  (to  give  the  proper  voltage  an  open 
circuit)  and  a  few  coils  of  thick  wire,  in  series  with  the 
main  circuit  (to  raise  the  excitation  in  proportion  to  the 
output),  the  voltage  may  be  kept  remarkably  constant. 
By  over-compounding  with  more  series  windings  the  dy- 
namo may  be  made  to  maintain  a  constant  voltage  at 
some  distant  point  in  the  circuit. 

468.  Constant  Current   Machines  —  Series  Lighting. 
—  To  maintain   an   unvarying   current    in    a   series   of 
lamps,    as   is   frequently  wanted   for   lighting   with   arc 
lamps  (Art.  448),  special  dynamos  are  used   known  as 
arc-lighting  machines.     The  best  known  of  these  are  the 
Brush  and  the  Thomson-Houston  dynamos.     Both  have 
open-coil  armatures  (in  which  the  coils  are  not  grouped 
in  a  closed  circuit),  with  special  commutators,  and  auto- 
matic devices  to  regulate  the  output,  the  one  by  shunting 
the  exciting  current,  the  other  by  shifting  the  brushes. 
The  current  may  thus  be  kept  at  10  amperes,  while  the 
volts  change  (according  to  the  number  of  lamps  in  circuit) 
from  50  to  2000  or  more. 

469.  Unipolar  Machines.  —  There   is  another  class 
of  dynamo-electric  machines,  differing  entirely  from  any 
of  the  preceding,  in  which  a  coil  or  other  movable  con- 
ductor slides  round  one  pole  of  a  magnet  and  cuts  the 
magnetic  lines  in  a  continuous  manner  without  any  re- 
versals in  the  direction  of  the  induced  currents.     Such 
machines,  sometimes  called  "  uni-polar  "  machines,  have, 
however,  very  low  electromotive-force,  and  are  not  prac- 
tical.    Faraday's   disk-machine    (Fig.   132)   belonged  to 
this  class. 


LESSON  XLIII.  —  Alternate  Currents 

47O.   Periodic   Currents.  —  We   have   seen   that   the 
revolving  of   a  simple  coil  in  a  magnetic  field  sets  up 


CHAP,  x  ALTERNATING   CURRENTS  487 

electromotive-forces,  which  change  in  direction  at  every 
half-turn,  giving  rise  to  alternate  currents.  In  each  whole 
revolution  there  will  be  an  electromotive-force  which 
rises  to  a  maximum  and  then  dies  away,  followed  imme- 
diately by  a  reversed  electromotive-force,  which  also 
grows  to  a  maximum  and  then  dies  away.  Each  such 
complete  set  of  operations  is  called  a  period,  and  the 
number  of  periods  accomplished  in  a  second  is  called  the 
frequency  or  periodicity  of  the  alternations,  and  is  symbol- 
ized by  the  letter  n.  In  2-pole  machines  n  is  the  same  as 
the  number  of  revolutions  per  second ;  but  in  multipolar 
machines  n  is  greater,  in  proportion  to  the  number  of  pairs 
of  poles.  By  revolving  in  a  uniform  field  the  electro- 
motive-forces set  up  are  proportional  to  the  sine  of  the 
angle  through  which  the  coil  has  turned  from  the  posi- 
tion in  which  it  lay  across  the  field.  If  in  this  position 
the  flux  of  magnetic  lines  through  it  were  N,  and  the 
number  of  spirals  in  the  coil  that  enclose  the  N  lines  be 
called  S,  then  the  value  of  the  induced  electromotive- 
force  at  any  time  t  when  the  coil  has  turned  through 
angle  0  (  =  2irn/)  will  be 

Ee  =  27rnSN  sin  0  -H-  108, 
or,  writing  D  for  27mSN/108,  we  have 
Ee  =--  D  sin  6. 

In  actual  machines  the  magnetic  fields  are  not  uni- 
form, nor  the  coils  simple  loops,  so  the  periodic  rise  and 
fall  of  the  electromotive-forces  will  not  necessarily  follow 
a  simple  sine  law.  The  form  of  the  impressed  waves 
will  depend  on  the  shape  of  the  polar  faces,  and  on  the 
form  and  breadth  of  the  coils.  But  in  most  cases  we 
are  sufficiently  justified  in  assuming  that  the  impressed 
electromotive-force  follows  a  sine  law,  so  that  the  value 
at  any  instant  may  be  expressed  in  the  above  form,  where 
D  is  the  maximum  value  or  amplitude  attained  by  E, 
and  0  an  angle  of  phase  upon  an  imaginary  circle  of 


ELECTRICITY  AND  MAGNETISM    PART 


reference.  Consider  a  point  P  revolving  clock-wise  round 
a  circle.  If  the  radius  of  this  circle  be  taken  as  unity, 
PM  will  be  the  sine  of  the  angle  0,  as  measured  from  0°. 
Let  the  circle  be  divided  into  any  number  of  equal  angles, 
and  let  the  sines  be  drawn  similarly  for  each.  Then  let 
these  sines  be  plotted  out  at  equal  distances  apart  along 
the  horizontal  line,  as  in  Fig.  251,  giving  us  the  sine 
curve. 

In  Fig.  251  one  revolution  of  P  around  the  circle  of 
reference  corresponds  to  one  complete  alternation  or  cycle 


Fig.  251. 

of  changes.  The  value  of  the  electromotive-force  (which 
varies  between  -f  D  and  —  D  as  its  maximum  values) 
may  be  represented  at  any  moment  either  by  the  sine 
PM  or  by  projecting  P  on  to  the  vertical  diameter,  giving 
OQ.  As  P  revolves,  the  point  Q  will  oscillate  along  the 
diameter. 

The  currents  which  result  from  these  periodic  or 
alternating  electromotive-forces  are  also  periodic  and 
alternating ;  they  increase  to  a  maximum,  then  die  away 
and  reverse  in  direction,  increase,  die  away,  and  then 
reverse  back  again.  If  the  electromotive-force  completes 
100  such  cycles  or  reversals  in  a  second,  so  also  will  the 
current. 

471.  Virtual  Volts  and  Virtual  Amperes.  —  Meas- 
uring instruments  for  alternate  currents,  such  as  elec- 
tro-dynamometers (Art.  395),  Cardew  voltmeters  (Art. 


CHAP,  x  LAG  AND  LEAD  489 

430),  and  electrostatic  voltmeters  (Art.  290)  do  not 
measure  the  arithmetical  average  values  of  the  amperes 
or  volts.  The  readings  of  these  instruments,  if  first 
calibrated  by  the  use  of  continuous  currents,  are  the 
square  roots  of  the  means  of  the  squares  of  the  values. 
They  measure  what  are  called  virtual  amperes  or  virtual 
volts.  The  mean  which  they  read  (if  we  assume  the 
currents  and  voltages  to  follow  the  sine  law  of  variation) 
is  equal  to  0-707  of  the  maximum  values,  for  the  average 
of  the  squares  of  the  sine  (taken  over  either  1  quadrant 
or  a  whole  circle)  is  |;  hence  the  square-root-of-mean- 
square  value  is  equal  to  1-*-  V2  times  their  maximum 
value.  If  a  voltmeter  is  placed  on  an  alternating  circuit 
in  which  the  volts  are  oscillating  between  maxima  of 
+  100  and  -  100  volts,  it  will  read  70-7  volts ;  and  70-7 
volts  continuously  applied  would  be  required  to  produce 
an  equal  reading.  If  an  alternate  current  amperemeter 
reads  100  amperes,  that  means  that  the  current  really 
rises  to  +  1414  amperes  and  then  reverses  to  —  1414 
amperes ;  but  the  effect  is  equal  to  that  of  100  continuous 
amperes,  and  therefore  such  a  current  would  be  described 
as  100  virtual  amperes. 

472.   Lag  and  Lead.  —  Alternating  currents  do  not 
always  keep  step  with  the  alternating  volts  impressed 


/x  /x 

o         \ 


Fig.  252. 

upon  the  circuit.  If  there  is  inductance  in  the  circuit 
the  currents  will  lag :  if  there  is  capacity  in  the  circuit 
they  will  lead  in  phase.  Fig.  252  illustrates  the  lag  pro- 
duced by  inductance.  The  impulses  of  current,  repre- 


490  ELECTRICITY   AND   MAGNETISM      PART  n 

sented  by  the  blacker  line,  occur  a  little  later  than  those 
of  the  volts.  But  inductance  has  another  effect  of  more 
importance  than  any  retardation  of  phase  ;  it  produces 
reactions  on  the  electromotive-force,  choking  the  current 
down.  While  the  current  is  increasing  in  strength  the 
reactive  effect  of  inductance  tends  to  prevent  it  rising. 
To  produce  a  current  of  40  amperes  in  a  resistance  of  \\ 
ohms  would  require  —  for  continuous  currents  —  an 
E.M.F.  of  60  volts.  But  an  alternating  voltage  of  60  volts 
will  not  be  enough  if  there  is  inductance  in  the  circuit 
reacting  against  the  voltage.  The  matter  is  complicated 
by  the  circumstance  that  the  reactive  impulses  of  electro- 
motive-force are  also  out  of  step  :  they  are  in  fact  exactly 
a  quarter  period  behind  the  current.  If  an  alternate  cur- 
rent of  C  (virtual)  amperes  is  flowing  with  a  frequency 
of  n  cycles  per  second  through  a  circuit  of  inductance  L, 
the  reactive  electromotive-force*  will  be  27rnLC  (virtual) 
volts.  If,  for  example,  L  =  0-002  henry,  n  =  50  periods 
per  second,  and  C  =  40  amperes,  the  reactive  electromo- 
tive-force will  be  25-1  volts.  Now  if  we  wish  to  drive 
the  40  (virtual)  amperes  not  only  through  the  resistance 
of  1*  ohms  but  against  this  reaction,  we  shall  require  more 
than  60  volts.  But  we  shall  not  require  60  +  25-1  volts, 
since  the  reaction  is  out  of  step  with  the  current.  Ohm's 
law  is  no  longer  adequate.  To  find  out  what  volts  will 
be  needed  we  have  recourse  to  geometry. 

Plot  out  (Fig.  253)  the  wave-form  OAbd,  to  correspond 
to  the  volts  necessary  to  drive  the  current  through  the 
resistance,  if  there  were  no  inductance.  The  ordinate 
a  A  may  be  taken  to  scale  as  60.  This  we  may  call  the 
current  curve.  Then  plot  out  the  curve  marked  —  jt>LC 
to  represent  the  volts  needed  to  balance  the  reaction  of 

*  This  is  calculated  as  follows.  From  Art.  458.  E  =  LdC/dt.  Now  C 
is  assumed  to  be  a  sine  function  of  the  time  having  instantaneous  value 
C0  sin  C2irnt ;  where  C0  is  the  maximum  value  of  0.  Differentiating  this  with 
respect  to  time  we  get  dC/dt  =  2nnC0  cos  2nnt.  The  "  virtual  "  values  of 
cosine  and  sine  being  equal  we  have  for  E  the  value  2n-nLC,  but  differing 
by  £  period  from  the  current  in  phase. 


PHASE   DIFFERENCES 


491 


the  inductance.  Here  p  is  written  for  lirn.  The  ordi- 
nate  at  O  is  25-1 ;  and  the  curve  is  shifted  back  one 
quarter  of  the  period :  for  when  the  current  is  increasing 
at  its  greatest  rate,  as  at  O,  the  self-inductive  action  is 
greatest.  Then  compound  these  two  curves  by  adding 


Pig.  253. 

their  ordinates,  and  we  get  the  dotted  curve,  with  its 
maximum  at  V.  This  is  the  curve  of  the  volts  that  must 
be  impressed  on  the  circuit  in  order  to  produce  the  cur- 
rent. It  will  be  seen  that  the  current  curve  attains  its 
maximum  a  little  after  the  voltage  curve.  The  current 
lags  in  phase  behind  the  volts.  If  Od 
is  the  time  of  one  complete  period,  the 
length  va  will  represent  the  time  that 
elapses  between  the  maxima  of  volts 
and  amperes.  In  Fig.  254  the  same 
facts  are  represented  in  a  revolving 
diagram  of  the  same  sort  as  Fig.  251. 
The  line  OA  represents  the  working 
volts  R  x  C,  whilst  the  line  AD  at  right  angles  to  OA 
represents  the  self-induced  volts  pLC.  Compounding 
these  as  by  the  triangle  of  forces  we  have  as  the  im- 
pressed volts  the  line  OD.  The  projections  of  these  3 
lines  on  a  vertical  line  while  the  diagram  revolves 
around  the  centre  O  give  the  instantaneous  values  of 
the  three  quantities.  The  angle  AOD,  or  <j>,  by  which 
the  current  lags  behind  the  impressed  volts  is  termed  the 


492 


ELECTRICITY   AND   MAGNETISM      PART  n 


angle  of  lag.  However  great  the  inductance  or  the  fre- 
quency, angle  <f>  can  never  be  greater  than  90°.  If 
OA  is  60  and  AD  is  254,  OD  will  be  65  volts.  In 
symbols,  the  impressed  volts  will  have  to  be  such  that 
E2  =  (RC)2  +  (  pLC)2.  This  gives  us  the  equation  :  — 

c=          E 

' 


The  denominator  which  comes  in  here  is  commonly  called 
the  impedance. 

473.   Maxwell's  Law.  —  In  Figs.  255  and  256   the 
angle  of  lag  is  seen  to  be  such  that  tan  <£  =pLC/RC  or 


/LC 


RC 

Fig.  255. 


R 

Fig.  256. 


=  _pL/R.  And  it  is  evident  that  the  effect  of  the  induct- 
ance is  to  make  the  circuit  act  as  if  its  resistance  instead 
of  being  R  was  increased  to  VR2  +  p*L*.  In  fact  tne  alter~ 
nate  current  is  governed  not  by  the  resistance  of  the 
circuit  but  by  its  impedance.  At  the  same  time  the  cur- 
rent is  lagging  as  if  the  angle  of  reference  were  not  6  but 
0  -  <f>,  so  that  the  equation  for  the  instantaneous  values 
of  C,  when  E  =  D  sin  0,  is 

D  sin       ~  * 


This  is  Maxwell's  law  for  periodic  currents  as  retarded 
by  inductance.  As  instruments  take  no  account  of  phase 
but  give  virtual  values  the  simpler  form  preceding  is 
usually  sufficient. 

The  effect  of  capacity  introduced  into  an  alternate 
current  circuit  is  to  produce  a  lead  in  phase,  since  the 
reaction  of  a  condenser  instead  of  tending  to  prolong  the 


CHAP.    X 


CHOKING  COILS 


493 


current  tends  to  drive  it  back.    The  reactance  is  therefore 

written  as  —  l/jt>K,  and  the  angle  <£  will  be  such   that 

tan  <£  =  - 1  /pli  R.     The  impedance  will  be  VR2+l/p2K2. 

If    both   inductance  and   capacity  are    present,    tan 


RC 


R 


<£  —  (jt?L  —  1//)K)/R;  the  reactance  will  be  />L  —  1/pK  ; 
and  the  impedance  VR2  +  (pL-l/pK)2. 

Since  capacity  and  inductance  produce  opposite  effects 
they  can  be  used  to  neutralize  one  another.  They  exactly 
balance  if  L  =  1//>2K.  In  that  case  the  circuit  is  non- 
inductive  and  the  currents  simply  obey  Ohm's  law. 

474.  Choking  Coils.  —  It  will  be  seen  that  if  in  a 
circuit  there  is  little  resistance,  and  much  reactance,  the 
current  will  depend  on  the  reactance.  For  example  if 
p(  =  27rn)  were,  say,  1000  and  L  =  10  henries  while  R  was 
only  1  ohm,  the  resistance  part  of  the  impedance  would 
be  negligible  and  the  law  would  become 

r     E 
'= 


Self-induction  coils  with  large  inductance  and  small  resist- 
ance are  sometimes  used  to  impede  alternate  currents,  and 
are  called  choking  coils,  or  impedance  coils. 

If  the  current  were  led  into  a  condenser  of  small 
capacity  (say  K=^  microfarad,  then  l/pK  =  10,000),  the 
current  running  in  and  out  of  the  condenser  would  be 
governed  only  by  the  capacity  and  frequency,  and  not  by 
the  resistance,  and  would  have  the  value  — 

C  =  Ejt?K. 
475.    Alternate-current  Power.  —  If  to  measure   the 


494  ELECTRICITY   AND   MAGNETISM      PART  n 

power  supplied  to  a  motor,  or  other  part  of  an  alternate 
current  circuit,  we  measure  separately  with  ampere- 
meter and  voltmeter  the  amperes  and  volts,  and  then 
multiply  together  the  readings  we  obtain  as  the  apparent 
watts  a  value  often  greatly  in  excess  of  the  true  ivatts, 
owing  to  the  difference  in  phase,  of  which  the  instruments 
take  no  account.  The  true  power  (watts)  is  in  reality 
W  =  CVcos<£,  where  C  and  V  are  the  virtual  values,  and 
<j)  the  angle  of  lag.  But  the  latter  is  usually  an  unknown 
quantity.  Hence  recourse  must  be  had  to  a  suitable 
watt-meter ;  the  usual  form  being  an  electrodynamometer 
(Art.  438)  specially  constructed  so  that  the  high-resistance 
circuit  in  it  shall  be  non-inductive. 

Whenever  the  phase-difference  (whether  lag  or  lead) 
is  very  large  the  current,  being  out  of  step  with  the  volts, 
is  almost  ivattless.  This  is  the  case  with  currents  flowing 
through  a  choking  coil  or  into  a  condenser,  if  the  resist- 
ances are  small. 

476.  High  Frequency  Currents.  —  The  reactive  effects 
of  inductance  and  capacity  increase  if  the  frequency 
is  increased.  The  frequency  used  in  electric  lighting  is 
from  50  to  120  cycles  per  second.  If  high  frequencies 
of  1000  or  more  cycles  per  second  are  used  the  reactions 
are  excessive.  In  such  cases  the  currents  do  not  flow 
equally  through  the  cross-section  of  the  conducting  wire, 
but  are  confined  mainly  to  its  outer  surface,  even  thick 
rods  of  copper  offering  great  impedance.  Even  at  a 
frequency  of  100  the  current  at  a  depth  of  12  millimetres 
from  the  surface  is  (in  copper)  only  about  }  of  its  value 
in  the  surface  layers.  In  iron  wires  the  depth  of  the 
skin  for  |  value  is  about  1  millimetre.  For  such  rapid 
oscillations  as  the  discharge  of  a  Leyden  jar,  where  the 
frequency  is  several  millions,  the  conducting  skin  is  prob- 
ably less  than  y^  of  a  millimetre  thick.  Hollow  tubes 
in  such  cases  conduct  just  as  well  as  solid  rods  of  same 
outer  diameter.  The  conductance  is  proportional  not  to 
section  but  to  perimeter. 


CHAP,  x     ALTERNATE-CURRENT  PHENOMENA     495 

Whenever  a  current  is  not  distributed  equally  in  the 
cross- section  of  any  conductor  there  is  a  real  increase  in 
the  resistance  it  offers ;  the  heating  effect  being  a  mini- 
mum when  equally  distributed.  The  fact  that  the 
oscillatory  currents  are  greatest  at  the  skin  gives  the 
strongest  support  to  the  modern  view  that  the  energy  in 
an  electric  circuit  is  transmitted  by  the  surrounding 
medium  and  not  through  the  wire  (see  Art.  519  on 
energy-paths). 

477.  Alternate-current  Electromagnets.  —  When  an 
alternate  current  is  sent  through  a  coil  it  produces  an 
alternating  magnetic  field.  An  iron  core  placed  in 
the  alternating  field  will  be  subjected  to  a  periodic 
alternating  magnetization.  Electromagnets  for  alter- 
nate currents  must  have  their  iron  cores  laminated  to 
avoid  eddy  currents ;  and  owing  to  their  choking  action 
are  made  with  fewer  turns  of  wire  than  if  designed 
for  continuous  currents  of  equal  voltage.  They  repel 
sheets  of  copper  owing  to  the  eddy  currents  which  they 
set  up  in  them ;  the  phase  of  these  eddy  currents  being 
retarded  by  their  self-induction.  Elihu  Thomson,  who 
studied  these  repulsions,  constructed  some  motors  based 
on  this  principle.  A  solenoid,  with  a  laminated  iron 
plunger,  if  supplied  with  alternate  currents  at  constant 
voltage,  has  the  remarkable  property  of  attracting  the 
core  with  much  greater  force  when  the  core  is  protruding 
out  than  when  it  is  in  the  tube.  This  also  is  owing  to 
the  choking  action. 


LESSON  XLIV. — Alternate-current  Generators 

478.  Alternators.  —  The  simple  alternator  (Fig.  243), 
with  its  two  slip-rings  for  taking  off  the  current,  is  merely 
typical.  In  practice  machines  are  wanted  which  will 
deliver  their  currents  at  pressures  of  from  1000  to  5000 
volts,  with  frequencies  of  from  50  to  120  cycles  per  second. 


496  ELECTRICITY  AND   MAGNETISM      PART  n 

Slower  frequencies  are  unsuitable  for  lighting,  though 
applicable  for  power  transmission.  High  voltages  are 
common  with  alternate  currents  because  (when  using 
transformers)  of  the  economy  (Art.  447)  thereby  effected 
in  the  copper  mains.  Under  these  conditions  almost  all 
alternators  are  designed  as  multipolar  machines ;  and  as 
the  perfect  insulation  required  in  the  armatures  is  more 
readily  attained  if  these  parts  are  stationary  it  is  common 
to  fix  them,  and  instead  to  rotate  the  field-magnet.  The 
latter  is  separately  excited  with  a  small  continuous  cur- 
rent led  in  through  slip-rings.  One  advantage  of  alter- 
nate current  machines  over  continuous  current  dynamos 
is  that  there  is  no  commutator. 

Amongst  the  various  types  of  alternators  may  be  men- 
tioned the  following: — (1)  Magnet  rotating  internally 
and  consisting  of  a  number  of  poles,  alternately  N  and  S, 
pointing  radially  outwards ;  armature  external,  fixed, 
and  consisting  of  a  number  of  coils  wound  either  upon 
an  iron  ring  (Gramme),  or  upon  inwardly  projecting  iron 
poles  (Ganz),  or  set  against  the  inner  face  of  an  iron  core 
(El well-Parker),  or  embedded  in  holes  just  within  the 
face  of  an  iron  core  (Brown).  In  all  cases  where  iron 
cores  are  used  in  armatures  it  is  carefully  laminated. 
(2)  Magnet  fixed  externally  and  consisting  of  a  number 
of  alternate  poles  pointing  radially  inwards ;  armature 
internal,  revolving,  consisting  of  a  number  of  coils  wound 
either  upon  the  surface  of  a  cylindrical  iron  core  (West- 
inghouse,  Thomson-Houston)  or  fixed  upon  radially  pro- 
jecting poles  (Hopkinson).  (3)  Magnet  fixed  externally 
and  consisting  of  two  crowns  of  alternate  poles,  alternately 
N  and  S,  projecting  toward  one  another  and  nearly  meet- 
ing, so  making  a  number  of  magnetic  fields  between  them ; 
armature  revolving,  and  without  iron,  consisting  of  a 
number  of  flat  coils  mounted  together  as  a  sort  of  star 
disk,  revolve  in  the  narrow  gaps  between  the  poles 
(Siemens,  Ferranti). 

Another  form,  known  as  Mordey's  alternator,  largely 


ALTERNATORS 


497 


used  in  England,  is  depicted  in  Fig.  259.  The  thiu 
armature  coils  are  fixed,  in  an  external  stationary  ring, 
between  two  crowns  of  poles  revolving  on  each  side  of 
them.  These  poles  are,  however,  all  N  poles  on  one  side, 
and  all  S  poles  on  the  other,  being  projections  of  two 
massive  iron  pole-pieces  fixed  on  the  shaft  against  a  huge 


Fig.  259. 

internal  bobbin,  thus  constituting  a  solid  simple  form  of 
field-magnet.  On  the  end  of  the  shaft  is  a  small  continu- 
ous-current dynamo  as  exciter. 

In  Fig.  260  is  given  a  view  of  the  central  generating 
station  for  the  electric  lighting  of  the  City  of  London. 
Two  kinds  of  alternators  (Thomson-Houston  and  Mordey) 
are  used.  The  cut  shows  one  of  the  latter  driven  by  an 
800  horse-power  steam-engine.  Each  of  these  machines 
has  40  poles  in  each  crown,  and  can  deliver  250  amperes 
at  2200  volts. 
2  K 


498 


ELECTRICITY   AND   MAGNETISM      PART  n 


CHAP,  x  COUPLING   OF   MACHINES  499 

479.  Coupling  of  Alternators.  —  In  the  use  of  two 
or  more  alternators  on  one  circuit  a  peculiarity  arises  that 
does  not  exist  with  continuous-current  dynamos,  owing  to 
differences  of  phase  in  the  currents.  If  two  alternators 
driven  by  separate  engines  are  running  at  the  same  speed 
and  at  equal  voltage,  it  will  not  do  to  join  their  circuits 
by  merely  switching  them  to  the  mains  if  they  are  not 
also  in  phase  with  one  another ;  or  serious  trouble  may 
occur.  In  central  station  work  it  is  usual  to  run  several 
machines  all  in  parallel.  Now  if  two  machines  are 
feeding  into  the  same  mains  each 
is  tending  to  send  current  back  to 
the  other ;  and  if  their  electro- 
motive-forces are  at  any  instant 
unequal,  that  with  the  greater  will 
tend  to  send  its  current  the  oppo- 
site way  through  the  other.  To 
explain  what  occurs  consider  Fig. 
261,  which  is  a  revolving  diagram 
of  the  same  kind  as  Figs.  251  and 
254.  If  the  two  alternators  are 

exactly  in  step,  they  will  both  be  sending  a  pulse  of  current 
toward  the  mains  at  the  same  moment,  but,  so  far  as  the 
circuit  connecting  them  is  concerned,  these  impulses  will 
be  exactly  opposed.  Let  OA  and  OB  represent  these 
two  exactly  opposed  impulses.  Now  suppose  one  of  the 
two  machines  to  gain  a  little  on  the  other,  OA  shifting 
forward  to  OA'.  The  two  electromotive-forces  no  longer 
balance,  but  will  have  a  resultant  OE  tending  to  make  a 
current  oscillate  through  the  two  machines,  this  current 
being  out  of  phase  both  with  the  leading  machine  A  and 
with  the  lagging  machine  B.  But  this  local  current  will 
itself  lag  a  little  in  phase  behind  OE  because  of  the  in- 
ductance in  its  path.  Let  the  phase  of  the  current  then 
be  indicated  by  OC,  which  is  set  back  a  little.  There  is 
now  a  current  surging  to  and  fro  between  the  two 
machines,  and  it  is  obviously  more  nearly  in  phase  with 


500  ELECTRICITY   AND   MAGNETISM      PART  n 

OA  than  with  OB.  This  means  that  in  the  leading 
machine  A  the  volts  and  amperes  are  more  nearly  in  phase 
with  one  another  than  in  the  lagging  machine  B.  Refer- 
ence to  Arts.  436  and  445  will  at  once  show  that  the  cur- 
rent is  helping  to  drive  B  as  a  motor,  and  that  a  greater 
mechanical  effort  will  be  thrown  on  A,  which  is  acting 
more  as  a  generator.  Hence  this  interchange  of  current 
tends  automatically  to  bring  up  the  lagging  machine  and 
to  load  the  leading  machine.  They  will  come  back  into 
phase.  All  alternators  of  good  construction  suitably 
driven  will  run  together  in  parallel,  even  though  their 
electromotive-forces  are  unequal.  On  the  other  hand,  if 
two  alternators  are  joined  in  series,  the  resulting  current, 
when  they  are  ever  so  little  out  of  phase,  tends  to  load  the 
lagging  machine  and  hasten  the  leading  one  till  they  get 
into  complete  opposition  of  phase,  one  running  entirely  as 
generator,  the  other  entirely  as  motor.  This  is  excellent 
for  transmission  of  power  from  an  alternator  at  one  end 
of  a  line  to  a  synchronous  alternator  at  the  other  :  the 
two  machines  keep  step  at  all  loads.  But  they  will  not 
run  together  in  series  if  both  are  to  act  as  generators, 
unless  rigidly  coupled  together  on  the  same  shaft. 

To  prevent  accidents  arising  from  too  sudden  a  trans- 
fer of  current  between  two  machines  it  is  usual  in  lighting 
stations  to  employ  a  synchronizer,  a  device  to  indicate  the 
phases  of  the  alternations.  When  an  alternator  is  to  be 
switched  into  circuit  (in  parallel  with  one  or  more  others) 
the  operator  does  not  turn  the  switch  until  (speed  and 
volts  being  both  right)  the  electromotive-force  of  the 
machine  has  come  exactly  into  identical  phase  with  that 
of  the  circuit  into  which  it  is  to  be  introduced. 

LESSON  XLV.  —  Transformers 

48O.  Alternate-current  Transformers.  —  Transform- 
ers are  needed  in  the  distribution  of  currents  to  a 
distance,  because  glow-lamps  in  the  houses  need  low 


CHAP.,  x  TRANSFORMERS  501 

pressures  of  50  to  100  volts,  whilst  for  economy  of  copper 
in  the  mains  it  is  necessary  that  the  generators  should 
work  at  high  pressures  of  1000  to  5000  or  more  volts. 
The  principle  of  transformation  was  briefly  touched  in 
Art.  228.  Alternate  current  transformers  are  simply 
induction-coils  having  well  laminated  iron  cores,  usually 
of  thin,  soft  sheet-iron  strips  piled  together,  and  shaped 
so  as  to  constitute  a  closed  magnetic  circuit.  Upon  the 
cores  are  wound  the  primary  coil  to  receive  the  alternat- 
ing current,  and  a  secondary  coil  to  give  out  other  alter- 
nating currents.  Usually  the  primary  consists  of  many 
turns  of  fine  copper  wire,  very  well  insulated,  to  receive 
a  small  current  at  high  pressure ;  and  the  secondary  of  a 
few  turns  of  thick  copper  wire  or  ribbon,  to  give  out  a 
much  larger  current  at  low  pressure. 

To  transform  down  from  about  2000  volts  to  100 
volts,  the  ratio  of  the  windings  will  be  20  : 1.  Whatever 
the  ratio  of  the  voltages,  the  currents  will  be  about  in  the 
inverse  ratio,  since,  apart  from  the  inevitable  small  losses 
in  transformation,  the  power  put  in  and  taken  out  will  be 
equal.  Taking  the  above  case  of  a  transformer  having 
20 : 1  as  the  ratio  of  its  windings,  if  we  desire  to  take  out 
of  the  secondary  100  amperes  at  50  volts,  we  must  put 
into  the  primary  at  least  5  amperes  at  1000  volts. 

In  scattered  districts  a  small  transformer  is  provided 
for  each  house,  the  lamps  being  in  the  low-pressure  cir- 


Alternator 

j[ 

Lout  Pressure  Mains 
Fig.  262. 

cuit.  In  cities  large  transformers  are  placed  in  sub- 
stations, from  which  issue  the  low-pressure  mains  dis- 
tributing the  current  to  the  houses.  Fig.  262  shows 


502  ELECTRICITY  AND   MAGNETISM      PART  n 

in  diagram  the  use  of  transformers  on  a  distributing 
system. 

481.  Elementary  Theory  of  Transformers.  —  If  the 
primary  volts  are  maintained  constant,  the  secondary 
volts  will  be  nearly  constant  also,  and  the  apparatus 
becomes  beautifully  self-regulating,  more  current  flow- 
ing into  the  primary  of  itself  when  more  lamps  are 
turned  on  in  the  secondary  circuit.  This  arises  from 
the  choking  effect  of  self-induction  in  the  primary.  If 
no  lamps  are  on  the  secondary  circuit  the  primary  coil 
simply  acts  as  a  choking-coil.  When  all  the  lamps  are 
on  the  primary  acts  as  a  working-coil  to  induce  currents 
in  the  secondary.  When  only  half  the  lamps  are  on 
the  primary  acts  partly  as  a  choking-coil  and  partly  as  a 
working-coil. 

Let  V,  be  the  volts  at  the  primary  terminals,  V2 
those  at  the  secondary  terminals  ;  St  the  number  of  turns 
in  the  primary  coil,  S2  the  number  in  the  secondary;  i\ 
the  internal  resistance  in  the  primary,  r2  that  of  the 
secondary.  Call  the  ratio  of  transformation  k  =  Sj/Sa- 
The  alternations  of  magnetism  in  the  core  will  set  up 
electromotive-forces  EL  and  E2  in  the  two  coils  strictly 
proportional  to  their  respective  numbers  of  turns  (if  there 
is  no  magnetic  leakage)  ;  so  E2  =  Ej/£;  and  since  (apart 
from  small  hysteresis  losses)  E^  =  E2C2,  it  follows  that 
Cj  =  G2/k.  The  volts  lost  in  primary  are  rjGv  those  in 
secondary  r2C2.  Hence  we  may  write 

V,  =  E,  +  riGv 

V2  =  E2  -  r2C2. 

Writing  the  first  as  Et  =  VL  -  r^  =  V}  -  rjC2/k, 
and  inserting  Ej/fc  for  E2  in  the  second  equation,  we  get 


which  shows  that  everything  goes  on  in  the  secondary  as 


CHAP,  x    TRANSFORMATIONS  OF  CURRENTS         503 


though  the  primary  had  been  removed,  and  we  had  sub- 
stituted for  Vj  a  fraction  of  it  in  proportion  to  the  wind- 
ings, and  at  the  same  time  had  added  to  the  internal 
resistance  an  amount  equal  to  the  internal  resistance  of 
the  primary,  reduced  in  proportion  to  the  square  of  the 
ratio  of  the  windings.  We  also  see  that  to  keep  the 
secondary  volts  constant  the  primary  generator  must  be 
so  regulated  as  to  cause  the  primary  volts  to  rise  slightly 
when  much  current  is  being  used.  The  currents  in  the 
two  coils  are  in  almost  exact  opposition  of  phase ;  they 
reach  their  maxima  at  the  same  instant,  flowing  in  oppo- 
site senses  round  the  core.  The  efficiency  of  well  con- 
structed transformers  is  very  high,  the  internal  losses 
being  a  very  small  percentage  of  the  working  load. 

482.  Continuous-current  Transformers    (Motor-dyna- 
mos) .  —  To    transform    continuous   currents   from    one 
voltage  to  another  it  is  necessary  to  employ  a  rotating 
apparatus,  which  is  virtually  a  combination  of  a  motor 
and  a  generator.     For  example,  a  motor  receiving  a  cur- 
rent of  10  amperes  at  1000  volts  may  be  made  to  drive  a 
dynamo  giving  out  nearly  200  amperes  at  50  volts.     In- 
stead of  using  two  separate  machines,  one  single  arma- 
ture  may  be  wound  with  two  windings  and  furnished 
with  two  commutators ;    the   number  of  turns  in  the 
windings  being  proportioned  to  the  voltages,  and  their 
sectional  areas  to  the  amperes.      Such  motor-dynamos  are 
in  use.     The  elementary  theory  of  these  is  the  same  as 
that  in  Art.  481,  E1  and  E2  now  standing  for  the  electro- 
motive-forces respectively  induced  in  the  two  windings 
on  the  revolving  armature. 

483.  Continuous-alternate    Transformers.  —  Revolv- 
ing  machinery  equivalent  to   a  combination  of   a  con- 
tinuous-current dynamo  and  an  alternator  may  be  used 
to   transform   continuous  currents   into   alternating,    or 
vice  versa,  one  part  acting  as  motor  to  drive,  the  other 
as  generator.     In  this  case  also  two  separate  machines 
need  not  always  be  used.    Fig.  263  represents  in  diagram 


504  ELECTRICITY  AND  MAGNETISM      PART  n 

a  simple  rotating  armature  having  both  a  split-tube  com- 
mutator to  collect  contin- 
uous currents,  and  a  pair 
of  slip-rings  or  alternating 
currents.  Such  a  machine 
may  convert  continuous 
currents  into  alternating, 
or  alternating  into  contin- 
uous. Or  it  may  act  as 
Fig  2C8.  a  motor  if  supplied  with 

either  kind  of  current ;  or 

may,  if  driven  mechanically,  generate  both  kinds  of  cur- 
rent at  the  same  time. 


LESSON  XL VI.  — Alternate-current  Motors 

484.  Alternate-current  Motors.  —  We  have  seen  (Art. 
479)  that  one  alternator  can  drive  another  as  a  motor, 
the    two    machines    in    series  working   in   synchronism. 
There  are  two  disadvantages  in  such  motors  —  (i.)  that 
they  are  not  self-starting,  but  must  be  brought   up  to 
speed  before  the  current  is  applied ;  (ii.)  that  their  field- 
magnets  must  be  separately  excited.   Other  forms  of  motor 
have  consequently  been  sought.      Ordinary  continuous- 
current  motors,  if  made  with   laminated  iron  magnets, 
will  work,  though  not  well,  with  alternating  currents. 

The  modern  alternate-current  motor  has  developed 
from  the  proposals  of  Borel  (1887),  Ferraris  (1888),  and 
Tesla  (1888)  to  employ  two  or  more  alternating  currents 
in  different  phases. 

485.  Polyphase  Currents.  — It  is  obviously  possible, 
by  placing  on  the  armature  of  an  alternator  two  sep- 
arate sets  of  coils,  one  a  little  ahead  of   the  other,  to 
obtain  two  alternate  currents  of  equal  frequency  and 
strength,  but  differing  in  phase  by  any  desired  degree. 
Gramme,  indeed,  constructed  alternators  with  two  and 


CHAP,  x    DI-PHASE  AND  TRI-PHASE  WORKING    505 


B 


with  three  separate  circuits  in  1878.  If  two  equal  alter- 
nate currents,  differing  in  phase  by  one-quarter  of  a 
period,  are  properly  combined,  they  can  be  made  to  pro- 
duce a  rotatory  magnetic  Jield.  And  in  such  a  rotatory 
field  conductors  can  be  set  rotating,  as  was  first 
suggested  by  Baily  in  1879.  Con- 
sider an  ordinary  Gramme  ring 
(  Fig.  264)  wound  with  a  continuous 
winding.  If  a  single  alternating 
current  were  introduced  at  the 
points  A  A'  it  would  set  up  an 
oscillatory  magnetic  field,  a  N  pole 
growing  at  A,  and  a  S  pole  at  A', 
then  dying  away  and  reversing  in 
direction.  Similarly,  if  another 

alternate  current  were  introduced  at  BB',  it  would 
produce  another  oscillatory  magnetic  field  in  the  BB' 
diameter.  If  both  these  currents  are  set  to  work  but 
timed  so  that  the  BB'  current  is  \  period  behind  the 
AA'  current,  then  they  will  combine 
to  produce  a  rotatory  magnetic  field, 
though  the  coil  itself  stands  still. 
This  is  quite  analogous  to  the  well- 
known  way  in  which  a  rotatory 
motion,  without  any  dead  points,  can 
be  produced  from  two  oscillatory 
motions  by  using  two  cranks  at  right 
angles  to  one  another,  the  impulses  being  given  \  period 
one  after  the  other.  The  above  combination  is  called 
a  di-phase  system  of  currents.  If  the  BB'  current  is 
\  period  later  than  the  AA'  current,  the  rotation  in 
Fig.  265  will  be  right-handed.  Another  way  of  generat- 
ing a  rotatory  field  is  by  a  tri-phase  system  *  (or  so-called 
"  dreh-strom ")  of  currents.  Let  3  alternate  currents, 
differing  from  one  another  by  £  period  (or  120°)  be  led 


Fig.  265. 


*  Tri-phase  currents  were  used  in  the  famous  Frankfort  transmission 
of  power  in  1891.    See  Art.  447. 


506  ELECTRICITY   AND   MAGNETISM      PART  11 

into  the  ring  at  the  points  ABC.  The  current  flows  in 
first  at  A  (and  out  by  B  and  C),  then  at  B  (flowing  out 
by  C  and  A),  then  at  C  (out  by  A  and  B),  again  produc- 
ing a  revolving  magnetic  field.  This  is  analogous  to  a 
3-crank  engine,  with  the  crank  set  at  120°  apart. 

There  are  several  ways  of  combining  the  circuits  that 
receive  the  currents  of  the  various  phases.  For  example, 
the  windings  of  Fig.  264  might  be  divided  into  four 
separate  coils,  each  having  one  end  joined  to  a  common 
junction,  and  the  four  outer  ends  joined  respectively  to 
the  four  line  wires.  Or  the  windings  of  Fig.  265  might 
be  arranged  as  three  separate  coils,  each  having  one  end 
joined  to  a  common  junction,  and  with  the  three  outer 
ends  joined  respectively  to  the  three  line  wires.  Such 
arrangements  would  be  called  star  groupings,  as  dis- 
tinguished from  the  mesh  groupings  of  the  cuts.  Also 
the  coils,  in  whichever  way  grouped,  need  not  be  wound 
upon  a  ring.  The  two-phase  coils  of  Fig.  264  might  be 
wound  upon  four  inwardly-projecting  pole-pieces;  and 
the  three-phase  coils  of  Fig.  265  might  be  wound  upon 
three  inwardly-projecting  pole-pieces.  Or  in  larger  mul- 
tipolar  machines  a  three-phase  set  of  coils  might  be 
arranged  upon  a  set  of  six,  nine,  twelve,  or  more  poles, 
in  regular  succession. 

486.  Properties  of  the  Rotatory  Field — Asynchronous 
Motors.  —  In  such  rotating  magnetic  fields  masses  of  metal 
at  once  begin  to  rotate.  A  magnet  or  mass  of  iron, 
pivoted  centrally,  can  take  up  a  synchronous  motion, 
but  may  require  to  be  helped  to  start.  Any  pivoted 
mass  of  good  conducting  metal,  such  as  copper,  will 
also  be  set  in  motion,  and  will  be  self-starting,  but 
will  not  be  synchronous.  In  such  a  centred  mass,  or 
rotor,  eddy-currents  are  set  up  (just  as  in  Arago's 
rotations,  Art.  457),  which  drag  the  metal  mass  and  tend 
to  turn  it.  The  strength  of  these  currents  in  the  rotating 
part  depends  on  the  relative  speed  of  the  field  and  the 
rotor.  If  the  rotor  were  to  revolve  with  speed  equal  to 


CHAP,  x  ASYNCHRONOUS   MOTORS  507 

the  revolving  field,  the  eddy-curreiits  would  die  away, 
and  there  would  be  no  driving  force.  The  rotor  actually 
used  in  such  motors  consists  of  a  cylindrical  core  built  up 
of  thin  iron  disks,  over  which  is  built  up  a  sort  of  squirrel 
cage  of  copper  rods  joined  together  at  their  ends  into  a 
closed  circuit.  In  some  forms  (designed  by  Brown)  the 
rods  are  inserted  in  holes  just  below  the  surface  of  the 
core.  The  revolving  part  has  no  commutator  or  slip- 
rings,  and  is  entirely  disconnected  from  any  other  circuit. 
It  receives  its  currents  wholly  by  induction.  Such 
asynchronous  motors  start  with  considerable  torque  (or 
turning  moment)  and  have  a  high  efficiency  in  full  work. 
Similar  motors  for  use  with  ordinary  or  single-phase 
alternate  currents  are  now  in  use.  To  start  them  it  is 
necessary  to  split  the  alternate  current  into  two  currents 
differing  in  phase.  This  is  done  by  the  use  of  a  divided 
circuit,  in  the  two  branches  of  which  different  reactances 
are  introduced.  If  in  one  branch  there  is  a  choking 
coil  to  offer  inductance,  the  current  in  that  branch  will 
be  retarded ;  if  in  the  other  there  is  a  condenser,  the 
current  in  this  branch  wrill  be  accelerated  in  phase.  Com- 
bining these  two  currents  a  rotatory  field  is  produced  for 
starting  the  movement.  When  once  the  motor  has  started 
a  further  turn  of  the  switch  simply  puts  on  the  alternate 
current,  as  at  AA'  in  Fig.  264,  and  it  continues  to  be 
driven,  though  the  impulse  is  now  only  oscillatory. 


CHAPTER  XI 

ELECTRO-CHEMISTRY 

LESSON  XL VII.  —  Electrolysis 

487.  Electromotive-force  of  Polarization.  —  The  sim- 
ple laws  of  definite  chemical  action  due  to  the  current 
having  been  laid  down  in  Lesson  XIX.  it  remains  to 
consider  the  relations  between  the  chemical  energy  and 
its  electrical  equivalent.  Whenever  an  electrolyte  is 
decomposed  by  a  current,  the  resolved  ions  have  a  ten- 
dency to  reunite,  that  tendency  being  commonly  termed 
"  chemical  affinity."  Thus  when  zinc  sulphate  (ZnSO4}  is 
split  up  into  Zn  and  SO4  the  zinc  tends  to  dissolve  again 
into  the  solution,  and  so  spread  the  potential  energy  of 
the  system.  But  zinc  dissolving  into  sulphuric  acid  sets 
up  an  electromotive-force  of  definite  amount ;  and  to  tear 
the  zinc  away  from  the  sulphuric  acid  requires  an  electro- 
motive-force at  least  as  great  as  this,  and  in  an  opposite 
direction  to  it.  So,  again,  when  acidulated  water  is 
decomposed  in  a  voltameter,  the  separated  hydrogen  and 
oxygen  tend  to  reunite  and  set  up  an  opposing  electro- 
motive-force of  no  less  than  1-47  volts.  This  opposing 
electromotive-force,  which  is  in  fact  the  measure  of  their 
"chemical  affinity,"  is  termed  the  electromotive-force  of 
polarization.  It  can  be  observed  in  any  water  voltameter 
(Art.  243)  by  simply  disconnecting  the  wires  from  the 
battery  and  joining  them  to  a  galvanometer,  when  a 
508 


CHAP,  xi       THEORY   OF   ELECTROLYSIS  509 

current  will  be  observed  flowing  back  through  the  volta- 
meter from  the  hydrogen  electrode  toward  the  oxygen 
electrode.  The  polarization  in  a  voltaic  cell  (Art.  175) 
produces  an  opposing  electromotive-force  in  a  perfectly 
similar  way. 

Now,  since  the  affinity  of  hydrogen  for  oxygen  is 
represented  by  an  electromotive-force  of  1'47  volts,  it  is 
clear  that  no  cell  or  battery  can  decompose  water  at 
ordinary  temperatures  unless  it  has  an  electromotive-force 
of  at  least  1-47  volts.  With  every  electrolyte  there  is  a 
similar  minimum  electromotive-force  necessary  to  produce 
complete  continuous  decomposition. 

488.  Theory  of  Electrolysis.  —  Suppose  a  current  to 
convey  a  quantity  of  electricity  Q  through  a  circuit  in 
which  there  is  an  opposing  electromotive-force  E :  the 
work  done  in  moving  Q  units  of  electricity  against  this 
electromotive-force  will  be  equal  to  E  x  Q.  (If  E  and 
Q  are  expressed  in  "  absolute  "  C.G.S.  units,  E  x  Q  will 
be  in  ergs.)  The  total  energy  of  the  current,  as  available 
for  producing  heat  or  mechanical  motion,  will  be  dimin- 
ished by  this  quantity,  which  represents  the  work  done 
against  the  electromotive-force  in  question. 

But  we  can  arrive  in  another  way  at  an  expression  for 
this  same  quantity  of  work.  The  quantity  of  electricity 
in  passing  through  the  cell  will  deposit  a  certain  amount 
of  metal:  this  amount  of  metal  could  be  burned,  or 
dissolved  again  in  acid,  giving  up  its  potential  energy  as 
heat,  and,  the  mechanical  equivalent  of  heat  being  known, 
the  equivalent  quantity  of  work  can  be  calculated.  Q 
units  of  electricity  will  cause  the  deposition  of  Qz  grammes 
of  an  ion  whose  absolute  electro-chemical  equivalent 
is  z.  [For  example,  z  for  hydrogen  is  -0001038  gramme, 
being  ten  times  the  amount  (see  Table  in  Art.  240) 
deposited  by  one  coulomb,  for  the  coulomb  is  T^  of  the 
absolute  C.G.S.  unit  of  quantity.]  If  II  represents  the 
number  of  heat  units  evolved  by  one  gramme  of  the  sub- 
stance, when  it  enters  into  the  combination  in  question, 


510  ELECTRICITY   AND   MAGNETISM       PART  n 

then  QzH  represents  the  value  (in  heat  units)  of  the 
chemical  work  done  by  the  flow  of  the  Q  units ;  and  this 
value  can  immediately  be  translated  into  ergs  of  work  by 
multiplying  by  Joule's  equivalent  J  ( =  42  x  106).  [See 
Table  on  page  512.] 

We  have  therefore  the  following  equality  :  — 

EQ  =  QzHJ;  whence  it  follows  that 

E  =  zll  J ;  or,  in  words,  the  electromotive-force  of  any 
chemical  reaction  is  equal  to  the  product  of  the  electro-chemical 
equivalent  of  the  separated  ion  into  its  heat  of  combination,  ex- 
pressed in  dynamical  units. 

Examples.* —  (1)  Electromotive-force  of  Hydrogen  tending 
to  unite  with  Oxygen.  For  Hydrogen  z  =  '0001038 ;  H 
(heat  of  combination  of  one  gramme)  —  34000  gramme- 
degree-units  ;  J  =  42  X  106. 

•0001038  X  31000  X  42  X  1Q6  =  1-48  X  1Q»  "  absolute  " 
units  of  electromotive-force,  or  =  1*48  volts. 

(2)  Electromotive-force  of  Zinc  dissolving  into  Sulphuric 
Acid,   z  =  -00337 ;  H  =  1670  (according  to  Julius  Thorn- 
sen)  ;   J  =  42  X  106. 

•00337  X  1070  X  42  X  10«  =  2 '364  X  HP, 
or  =  2-364  volts. 

(3)  Electromotive-force  of  Copper  dissolving  into  Sulphuric 
Acid,    z  =  '00327 ;  H  =  909-5 ;  J  -  42  x  106. 

•00327  X  909-5  X  42  X  10«  =  1-249  X  10«, 
or  =  1-249  volts. 

(4)  Electromotive-force  of  a  Daniell's  Cell.    Here  zinc  is 
dissolved  at  one  pole  to  form  zinc  sulphate,  the  chemi- 
cal action  setting  up  a  +  electromotive-force,  while  at 
the  other  pole  copper  is  deposited  by  the  current  out  of  a 

*  The  figures  given  in  these  examples  as  well  as  those  on  p.  512  for 
the  heat  of  combination  must  be  taken  as  only  approximate.  The  heat  of 
combination  is  different  at  different  temperatures,  and  the  heat  evolved 
by  the  salt  dissolving  in  water  must  also  be  taken  into  account.  Exact 
figures  have  not  yet  been  ascertained.  In  fact  Von  llelmholtz  showed 
that  the  expression  01IJ  is  incomplete,  and  that  to  it  should  be  added  a 
term  6-dE/dO,  wherein  9  is  the  absolute  temperature  of  the  cell. 


CHAP,  xi      CONSUMPTION  OF  CHEMICALS  511 


solution  of  copper  sulphate,  thereby  setting  up  an 
opposing  (or  —  )  electromotive-force.  That  due  to  zinc 
is  shown  above  to  be  +  2'364:  volts,  that  to  deposited 
copper  to  be  —  T249.  Hence  the  net  electromotive- 
force  of  the  cell  is  (neglecting  the  slight  electromotive- 
force  where  the  two  solutions  touch)  2'364  —  T2-19  = 
1-115  volts.  This  is  nearly  what  is  found  (Art,  181)  in 
practice  to  be  the  case.  It  is  less  than  will  suffice  to 
electrolyze  water,  though  two  Daniell's  cells  in  series 
electrolyze  water  easily. 

Since  1  horse-power-hour  =  746  watt-hours  =  746  am- 
pere-hours at  1  volt,  it  follows  that  at  V  volts  the  num- 
ber of  ampere-hours  will  =  746  -^-  V.  Now  as  the  weight 
of  zinc  consumed  in  a  cell  is  1-213  grammes  per  ampere- 
hour  (when  there  is  no  waste)  the  consumption  will  be 
as  follows :  — 

Weight  of  zinc  used  \  =  746  x  ^^  =  2^ 

per  horse-power-hour )        V  V 

Hence  the  quantity  of  zinc  that  must  be  consumed  to 
generate  1  horse-power-hour  in  any  battery  of  cells  cannot 
be  less  than  2  Ibs.  -f-  the  available  volts  of  a  single  cell  of 
the  battery. 

Example.  —  If  a  new  cell  can  be  invented  to  give  2  volts  at  its  terminals 
when  in  full  work,  a  battery  of  such  cells,  however  arranged,  will 
consume  1  Ib.  of  zinc  per  hour  per  horse-power,  or  1'34  Ibs.  per 
"  unit "  of  supply  (or  kilowatt-hour). 

An  equivalent  quantity  of  exciting  and  depolarizing 
chemicals  will  also  be  used,  and  these  will  increase  the 
total  cost  per  unit.  It  is  clear  that  as  a  source  of  public 
supply  primary  batteries  consuming  zinc  can  never  com- 
pete in  price  with  dynamos  driven  by  steam.  The  actual 
cost  of  coal  to  central  stations  in  London  is  from  1  to 
1|  pence  per  "  unit  "  ;  and  the  maximum  legal  price  that  a 
supply  company  may  charge  in  Great  Britain  for  electric 
energy  is  eightpence  per  "unit  "  (see  Art.  440). 

489.  Electro-Chemical  Power  of  Metals.  —  The  ac- 
companying Table  gives  the  electromotive-force  of  the 


612 


ELECTRICITY   AND   MAGNETISM      TART  n 


different  metals  as  calculated  (Art.  488)  from  the  heat 
evolved  by  the  combination  with  oxygen  of  a  portion  of 
the  metal  equivalent  electro-chemically  in  amount  to  one 
gramme  of  hydrogen.  The  figures  in  the  second  column 
are  in  calories.  The  figures  in  the  third  column  are 
calculated  from  these  in  the  second  by  multiplying  by 
the  electro-chemical  equivalent  of  hydrogen,  and  by 
Joule's  equivalent  (42  x  106)  and  dividing  by  108,  to 
reduce  to  volts.  The  electromotive-forces  as  observed  (in 
dilute  sulphuric  acid)  are  added  for  comparison. 


E.M.F.  calculated. 

Heat  of  Oxi- 

E M  F 

Substance. 

dation  of 
Equivalent. 

Relatively 

to  Oxygen. 

Relatively 
to  Zinc. 

observed. 

Potassium    .    .    . 

69,800 

3-01 

+1-18 

+1-13 

Sodium    .  '.     .     . 

67,800 

2-91 

+1-09 

Zinc      

42,700 

1-83 

o- 

o- 

Iron     

34,120 

1-55 

-0'28 

Hydrogen     .     .     . 

34,000 

1-47 

-0-36 

Lead 

25,100 

1*12 

—  0*71 

—  0'54 

Copper     .... 

18,760 

•80 

-1-08 

—1-047 

Silver  

9,000 

•39 

—1-44 

Platinum      .     .     . 

7,500 

•33 

-1-50 

—1-53 

Carbon     .... 

2,000 

•09 

—1-74 

Oxygen    .... 
(Nitric  Acid)     .     . 

0 

-  6,000 

o- 

-0-26 

-1-83 
—2-09 

—1-85 
-1-94 

(Black    Oxide    of 

Manganese)  .     . 
(Peroxide  of  Lead) 
(Ozone)    .... 

—  6,500 
—12,150 
—14,800 

-0-29 
—0-52 
—0-63 

-2-12 
-2-35 
—2-46 

—2-23 
—2-52 
—2-64 

(Permanganic 
Acid)     .... 

—25,070 

—1-09 

-2-92 

—3-03 

1 

The  order  in  which  these  metals  are  arranged  is  in 
fact  nothing  else  than  the  order  of  oxidizability  of  the 
metals  (in  the  presence  of  dilute  sulphuric  acid)  ;  for  that 
metal  tends  most  to  oxidize  which  can,  by  oxidizing,  give 
out  the  most  energy.  It  also  shows  the  order  in  which 


CHAP,  xi    LAWS  OF  ELECTROLYTIC  ACTION         513 

the  metals  stand  in  their  power  to  replace  one  another 
(in  a  solution  containing  sulphuric  acid).  In  this  order, 
too,  the  lowest  on  the  list  are  the  metals  deposited  first 
by  an  electric  current  from  solutions  containing  two  or 
more  of  them  :  for  that  metal  comes  down  first  which 
requires  the  least  expenditure  of  energy  to  separate  it 
from  the  elements  with  which  it  was  combined. 

490.  General  Laws  of  Electrolytic  Action.  —  In  addi. 
tion  to  Faraday's  quantitative  laws  given  in  Art.  240, 
the  following  are  important :  — 

(a.)  Every  electrolyte  is  decomposed  into  two  portions, 
an  anion  and  a  kation,  which  may  be  themselves  either 
simple  or  compound.  In  the  case  of  simple  binary  com- 
pounds, such  as  fused  salt  (NaCl),  the  ions  are  simple 
elements.  In  other  cases  the  products  are  often  compli- 
cated by  secondary  actions.  It  is  even  possible  to  deposit 
an  alloy  of  two  metals  —  brass  for  example  —  from  a 
mixture  of  the  cyanides  of  zinc  and  of  copper. 

(6.)  In  binary  compounds  and  most  metallic  solutions, 
the  metal  is  deposited  by  the  current  where  it  leaves  the 
cell,  at  the  kathode. 

(c.)  Aqueous  solutions  of  salts  of  the  metals  of  the 
alkalies  and  alkaline  earths  deposit  no  metal,  but  evolve 
hydrogen  owing  to  secondary  action  of  the  metal  upon 
the  water.  From  strong  solutions  of  caustic  potash  and 
soda  Davy  succeeded  in  obtaining  metallic  sodium  and 
potassium,  which  were  before  unknown.  If  electrodes  of 
mercury  are  employed,  an  amalgam  of  either  of  these 
metals  is  readily  obtained  at  the  kathode.  The  so-called 
ammonium-amalgam  is  obtained  by  electrolyzing  a  warm, 
strong  solution  of  sal  ammoniac  between  mercury  elec- 
trodes. 

(d.)  Metals  can  be  arranged  in  a  definite  series  accord- 
ing to  their  electrolytic  behaviour  ;  each  metal  on  the  list 
behaving  as  a  kation  (or  being  "  electropositive  ")  when 
electrolyzed  from  its  compound  in  preference  to  one 
lower  down  on  the  list.  In  such  a  series  the  oxidizable 
2  L 


514  ELECTRICITY   AND    MAGNETISM      PART  n 

metals,  potassium,  sodium,  zinc,  etc.,  come  last ;  the  less 
oxidizable  or  "electronegative"  metals  preceding  them. 
The  order  varies  with  the  nature,  strength,  and  tempera- 
ture of  the  solution  used. 

(e.)  From  a  solution  of  mixed  metallic  salts  the  least 
electropositive  metal  is  not  deposited  first,  if  the  current 
is  so  strong  relatively  to  the  size  of  the  kathode  as  to 
impoverish  the  solution  in  its  neighbourhood.  To  deposit 
alloys  a  solution  must  be  found  in  which  both  metals 
tend  to  dissolve  with  equal  electromotive-forces. 

(/.)  The  liberated  ions  appear  only  at  the  electrodes. 

(<7.)  For  each  electrolyte  a  minimum  electromotive-force 
is  requisite,  without  which  complete  electrolysis  cannot  be 
effected.  (See  Art.  491.) 

(h.)  If  the  current  be  of  less  electromotive-force  than 
the  requisite  minimum,  electrolysis  may  begin,  and  a 
feeble  current  flow  at  first,  but  110  ions  will  be  liberated, 
the  current  being  completely  stopped  as  soon  as  the 
opposing  electromotive-force  of  polarization  has  risen  to 
equality  with  that  of  the  electrolyzing  current. 

({.)  There  is  no  opposing  electromotive-force  of  polar- 
ization when  electrolysis  is  effected  from  a  dissolving 
anode  of  the  same  metal  that  is  being  deposited  at  the 
kathode.  The  feeblest  cell  will  suffice  to  deposit  copper 
from  sulphate  of  copper  if  the  anode  be  a  copper  plate. 

00  Where  the  ions  are  gases,  pressure  affects  the 
conditions  but  slightly.  Under  300  atmospheres  acid- 
ulated water  is  still  electroly/ed ;  but  in  certain  cases  a 
layer  of  acid  so  dense  as  not  to  conduct  collects  at  the 
anode  and  stops  the  current. 

(fc.)  The  chemical  work  done  by  a  current  in  an 
electrolytic  cell  is  proportional  to  the  minimum  electro- 
motive-force of  polarization. 

(/.)  Although  the  electromotive-force  of  polarization 
may  exceed  this  minimum,  the  work  done  by  the  current 
in  overcoming  this  surplus  electromotive-force  will  not 
appear  as  chemical  work,  for  no  more  of  the  ion  will  be 


CHAP,  xi       HYPOTHESIS   OF   GROTTHUSS  515 

liberated;  but  it  will  appear  as  an  additional  quantity 
of  heat  (or  "  local  heat ")  developed  in  the  electrolytic 
cell. 

(m.)  Ohm's  law  holds  good  for  electrolytic  conduction. 

(n.)  Amongst  the  secondary  actions  which  may  occur 
the  following  are  the  chief  :  — 

(1)  The  ions  may  themselves  decompose ;  as  SO4  into  SO3  +  O. 
(2)  The  ions  may  react  on  the  electrodes ;  as  when  acidulated 
water  is  electrolyzed  between  zinc  electrodes,  no  oxygen  being 
liberated,  owing  to  the  affinity  of  zinc  for  oxygen.  (3)  The  ions 
may  be  liberated  in  an  abnormal  state.  Thus  oxygen  is  fre- 
quently liberated  in  its  allotropic  condition  as  ozone,  particu- 
larly when  permanganates  are  electrolyzed.  The  "nascent" 
hydrogen  liberated  by  the  electrolysis  of  dilute  acid  has  pecul- 
iarly active  chemical  properties.  So  also  the  metals  are  some- 
times deposited  abnormally:  copper  in  a  black  pulverulent 
film ;  antimony  in  roundish  gray  masses  (from  the  terchloride 
solution)  which  possess  a  curious  explosive  property.  When  a 
solution  of  lead  is  electrolyzed  a  film  of  peroxide  of  lead  forms 
upon  the  anode.  If  this  be  a  plate  of  polished  metal  placed 
horizontally  in  the  liquid  beneath  a  platinum  wire  as  a  kathode, 
the  deposit  takes  place  in  symmetrical  rings  of  varying  thick- 
ness,  the  thickest  deposit  being  at  the  centre.  These  rings, 
known  as  Nobili's  rings,  exhibit  all  the  tints  of  the  rainbow, 
owing  to  interference  of  the  waves  of  light  occurring  in  the  film. 
The  colours  form,  in  fact,  in  reversed  order,  the  "  colours  of 
thin  plates  "  of  Newton's  rings. 

491.  Hypotheses  of  Grotthuss  and  of  Clausius.  —  A 
complete  theory  of  electrolysis  must  explain  — firstly, 
the  transfer  of  electricity,  and  secondly,  the  transfer 
of  matter,  through  the  liquid  of  the  cell.  The  latter 
point  is  the  one  to  which  most  attention  has  been 
given,  since  the  "  migration  of  the  ions  "  (i.e.  their  trans- 
fer through  the  liquid)  in  two  opposite  directions,  and 
their  appearance  at  the  electrodes  only,  are  salient  facts. 

The  hypothesis  put  forward  in  1805  by  Grotthuss 
serves  fairly,  when  stated  in  accordance  with  modern 
terms,  to  explain  these  facts.  Grotthuss  supposes  that, 
when  two  metal  plates  at  different  potentials  are  placed 


516 


ELECTRICITY  AND   MAGNETISM      PART  n 


in  a  cell,  the  first  effect  produced  in  the  liquid  is  that 
the  molecules  of  the  liquid  arrange  themselves  in  in- 
numerable chains,  in  which  every  molecule  has  its 
constituent  atoms  pointing  in  a  certain  direction;  the 
atom  of  electropositive  substance  being  attracted  toward 
the  kathode,  and  the  fellow  atom  of  electronegative 
substance  being  attracted  toward  the  anode.  (This 
assumes  that  the  constituent  atoms  grouped  in  the  mole- 
cule retain  their  individual  electric  properties.)  The 
diagram  of  Fig.  266  shows,  in  the  case  of  hydrochloric 


"JZL 


Fig.  260. 

acid,  a  first  row  of  molecules  distributed  at  random,  and 
secondly  grouped  in  a  chain  as  described.  The  action 
which  Grotthuss  then  supposes  to  take  place  is  that  an  in- 
terchange of  partners  goes  on  between  the  separate  atoms 
all  along  the  line,  each  H  atom  uniting  with  the  Cl  atom 
belonging  to  the  neighbouring  molecule,  a  -f  half  mole- 
cule of  hydrogen  being  liberated  at  the  kathode,  and  a  — 
half  molecule  of  chlorine  at  the  anode.  This  action 
would  leave  the  molecules  as  in  the  third  row,  and 
would,  when  repeated,  result  in  a  double  migration  of 
hydrogen  atoms  in  one  direction  and  of  chlorine  atoms 


CHAP,  xi       ELECTROLYTIC   CONVEXION  517 

in  the  other ;  the  free  atoms  appearing  only  at  the  elect- 
rodes, and  every  atom  so  liberated  discharging  a  certain 
definite  minute  charge  of  electricity  upon  the  electrode 
where  it  was  liberated.* 

Clausius  sought  to  bring  the  ideas  of  Grotthuss  into 
conformity  with  the  modern  kinetic  hypothesis  of  the 
constitution  of  liquids.  He  supposes  that  in  the  usual 
state  of  a  liquid  the  molecules  are  always  gliding  about 
amongst  one  another,  and  their  constituent  atoms  are 
also  in  movement,  continually  separating  and  recombining 
into  similar  groups,  their  movements  taking  place  in  all 
possible  directions  throughout  the  liquid.  But  under 
the  influence  of  an  electromotive-force  these  actions  are 
controlled  in  direction,  so  that  when,  in  the  course  of  the 
usual  movements,  an  atom  separates  from  a  group  it 
tends  to  move  either  toward  the  anode  or  kathode; 
and  if  the  electromotive-force  in  question  be  powerful 
enough  to  prevent  recombination,  these  atoms  will  be 
permanently  separated,  and  will  accumulate  around  the 
electrodes.  This  theory  has  the  advantage  of  account- 
ing for  a  fact  easily  observed,  that  an  electromotive-force 
less  than  the  minimum  which  is  needed  to  effect  com- 
plete electrolysis  may  send  a  feeble  current  through  an 
electrolyte  for  a  limited  time,  until  the  opposing  electro- 
motive-force has  reached  an  equal  value.  Von  Helmholtz, 
who  gave  the  name  of  electrolytic  connexion  to  this  pheno- 
menon of  partial  electrolysis,  assumed  that  it  takes  place 
by  the  agency  of  uncombined  atoms  previously  existing 
in  the  liquid. 

*  Mr.  G.  J.  Stoney  has  reckoned,  from  considerations  founded  on 
the  size  of  atoms  (as  calculated  by  Loschraidt  and  Lord  Kelvin),  that 
for  every  chemical  bond  ruptured,  a  charge  of  10—20  of  a  coulomb  is 
transferred.  [E.  Budde  says  IT  x  10-20  coulomb.]  This  quantity  would 
appear  therefore  to  be  the  natural  atomic  charge  or  unit.  To  tear  one 
atom  of  hydrogen  from  a  hydrogen  compound  this  amount  of  electricity 
must  be  sent  through  it.  To  liberate  an  atom  of  zinc,  or  any  other  diva- 
lent metal  from  its  compound,  implies  the  transfer  of  twice  this  amount 
of  electricity. 


518 


ELECTRICITY   AND   MAGNETISM      PART  11 


LESSON  XLVIII.  —  Accumulators 

492.  Accumulators  or  Secondary  Batteries.  —  A 
voltameter,  or  series  of  voltameters,  whose  electrodes 
are  thus  charged  respectively  with  hydrogen  and  oxygen, 
will  serve  as  secondary  batteries,  in 
which  the  energy  of  a  current 
may  be  stored  up  and  again  given 
out.  Ritter,  who  in  1803  con- 
structed a  secondary  pile,  used 
electrodes  of  platinum.  It  will 
be  seen  that  such  cells  do  not 
accumulate  or  store  electricity; 
what  they  accumulate  is  energy, 
which  they  store  in  the  form  of 
chemical  work.  A  secondary  cell 
resembles  a  Ley  den  jar  in  that 
it  can  be  charged  and  then  dis- 
charged. The  residual  charges  of 
Leyden  jars,  though  small  in 
quantity  and  transient  in  their 
discharge,  yet  exactly  resemble 
the  polarization-charges  of  volta- 
meters. Varley  found  1  sq.  cen- 
tim.  of  platinum  foil  in  dilute 
acid  to  act  as  a  condenser  of 
about  63  microfarads  capacity, 
when  polarized  to  a  potential- 
difference  of  1  volt.  Gaston  Plante,  in  1860,  devised  a 
secondary  cell  consisting  of  two  pieces  of  sheet  lead 
rolled  up  (without  actual  contact)  as  electrodes,  dipping 
into  dilute  sulphuric  acid,  as  in  Fig.  267.  To  "  form  " 
or  prepare  the  lead  it  was  charged  with  currents  'which 
after  a  time  were  reversed  in  direction,  and  after  a  further 
time  again  reversed  until,  after  several  reversals,  it  became 
coated  with  a  semi-porous  film  of  brown  dioxide  of  lead 


Fig.  267. 


CHAP.    XI 


ACCUMULATORS 


519 


on  the  anode  plate ;  the  kathode  plate  assuming  a  spongy 
metallic  state  presenting  a  large  amount  of  surface  of 
high  chemical  activity.  When  such  a  secondary  battery, 
or  accumulator,  is  charged  by  connecting  it  with  a  dynamo 
(shunt-wound),  or  other  powerful  generator  of  currents, 
the  anode  plate  becomes  peroxidized,  while  the  kathode 
plate  is  deoxidized  by  the  hydrogen  that  is  liberated. 
The  plates  may  remain  for  many  days  in  this  condition, 
and  will  furnish  a  current  until  the  two  lead  surfaces 
are  reduced  to  a  chemically  inactive  state.  The  electro- 
motive-force of  such  cells  is  from  2-0  to  1-85  volts  during 
discharge.  Plante  ingeniously  arranged  batteries  of  such 
cells  so  that  they  can  be  charged  in  parallel,  and  dis- 
charged in  series,  giving  (for  a  short  time)  strong  currents 
at  extremely  high  voltages.  Faure,  in  1881,  modified 
the  Plante  accumulator  by  giving  the  two  lead  plates  a 
preliminary  coating  of  red-lead  (or  minium).  When  a 
current  is  passed  through  the  cell  to  charge  it,  the  red- 
lead  is  peroxidized  at  the  anode,  and  reduced,  —  first  to  a 
condition  of  lower  oxide, 
then  to  the  spongy  metallic 
state, — at  the  kathode,  and 
thus  a  greater  thickness  of 
the  working  substance  is 
provided,  and  takes  far 
less  time  to  "  form  "  than 
is  the  case  in  Plante's  cells. 
In  modern  accumulators 
the  red-lead  (or  litharge), 
freshly  mixed  with  dilute 
sulphuric  acid  to  the  form 
of  a  paste,  is  pressed  into 
the  holes  of  a  leaden  grid, 
shaped  so  as  to  give  it  a  Fig-  268> 

good  mechanical  attachment.  During  the  subsequent 
process  of  "formation"  the  hardened  paste  is  reduced 
on  one  plate  and  peroxidized  on  the  other.  A  cell  of  the 


520  ELECTRICITY  AND  MAGNETISM      PART  n 

kind  known  as  the  E.P.S.  cell  is  shown  in  Fig.  268. 
Accumulators  are  still  made  on  the  Plante  method  from 
metallic  lead,  which  is  first  finely  divided  on  its  sur- 
face by  some  mechanical  or  chemical  means,  and  then 
"  formed  "  by  prolonged  charging.  Cells  of  this  type  are 
not  so  subject  to  disintegration  as  paste  cells,  and  may  be 
discharged  at  a  greater  rate.  To  keep  accumulators  in 
good  condition  they  should  be  charged  up  every  day  till 
full  (known  by  bubbles  rising)  and  not  be  discharged  too 
quickly.  The  density  of  acid  should  never  be  allowed 
to  exceed  1-21  nor  fall  below  1-15. 

493.  Grove's  Gas  Battery.  — Sir  W.  Grove  devised  a 
cell  in  which  platinum  electrodes,  in  contact  respectively 
with  hydrogen  and  oxygen  gas,  replaced  the  usual  zinc 
and  copper  plates.      Each   of  these   gases   is   partially 
occluded  by  the  metal  platinum,  which,  when  so  treated, 
behaves  like  a  different  metal. 

Attempts  have  been  made  to  generate  electricity  on 
a  larger  scale  by  means  of  gas  batteries.  Mond  and 
Langer  found  that  the  greatest  E.M.F.  to  be  obtained 
from  a  cell  of  hydrogen  and  oxygen,  with  finely  divided 
platinum  as  collectors,  was  0-97,  the  difference  between 
this  and  the  theoretical,  147,  being  lost  in  heat  generated 
by  the  condensation  of  the  gases  by  the  platinum. 

LESSON  XLIX.  —  Electrodeposition 

494.  Electrometallurgy.  —  The  applications  of  electro- 
chemistry to  the  industries  are  threefold.     Firstly,  to  the 
reduction  of  metals  from  solutions  of  their  ores,  the  pro- 
cess is  useful  in  the  accurate  assay  of  certain  ores,  as,  for 
example,  of  copper;   secondly,  to  the  copying  of  types, 
plaster  casts,  and  metal-work  by  kathode   deposits   of 
metal ;  thirdly,  to  the  covering  of  objects  made  of  baser 
metal  with  a  thin  film  of  another  metal,  such  as  gold, 
silver,  or  nickel.    All  these  operations  are  included  under 
the  general  term  of  electrometallurgy. 


CHAP,  xi  ELECTROTYPING  521 

It  is  not  established  whether  the  reduction  of  aluminium 
in  the  electric  furnace  is  partly  electrolytic  or  whether  it 
is  purely  chemical,  but  the  process  may  be  mentioned 
here.  Aluminium  oxide  is  mixed  with  charcoal  and 
placed  between  the  ends  of  two  thick  carbon  rods  in  a 
closed  firebrick  furnace  lined  with  charcoal.  A  current 
of  several  thousand  amperes  is  passed  between  the  carbon 
rods  and  the  aluminium  ore  is  melted  and  parts  with  its 
oxygen  to  carbon.  The  liberated  aluminium  is  commonly 
allowed  to  alloy  with  some  other  metal,  such  as  copper, 
previously  added  to  the  charge,  and  forms  the  famous 
aluminium  bronze.  Pure  aluminium  is  now  produced  in 
large  quantities  by  the  electrolysis  of  fused  cryolite, 
which  is  a  double  fluoride  of  aluminium  and  sodium. 

Copper  of  a  high  degree  of  purity  is  produced  on  a 
large  scale  by  suspending  anodes  of  impure  copper  in  a 
solution  of  copper  sulphate  and  electrolytically  depositing 
pure  copper  on  the  kathodes.  The  impurities  such  as 
arsenic  being  more  electronegative  than  copper  are  left 
in  the  bath. 

495.  Electrotyping.  —  In  1836  De  La  Rue  observed 
that  in  a  Daniell's  cell  the  copper  deposited  out  of  the 
solution  upon  the  copper  plate  which  served  as  a  kathode 
took  the  exact  impress  of  the  plate,  even  to  the  scratches 
upon  it.  In  1839  Jacobi  in  St.  Petersburg,  Spencer  in 
Liverpool,  and  Jordan  in  London,  independently  devel- 
oped out  of  this  fact  a  method  of  obtaining,  by  the 
electrolysis  of  copper,  impressions  (in  reversed  relief)  of 
coins,  stereotype  plates,  and  ornaments.  A  further  im- 
provement, due  to  Murray,  was  the  employment  of 
moulds  of  plaster  or  wax,  coated  with  a  film  of  plumbago 
in  order  to  provide  a  conducting  surface  upon  which  the 
deposit  could  be  made.  Bronze  in  the  form  of  a  fine 
powder  is  much  used  instead  of  plumbago,  being  a  better 
conductor.  Jacobi  gave  to  the  process  the  name  of  galuano- 
plastic,  a  term  generally  abandoned  in  favour  of  the  term 
electrotyping  or  electrotype  process. 


522  ELECTRICITY  AND   MAGNETISM      PART  n 

Electrotypes  of  copper  are  easily  made  by  hanging  a 
suitable  mould  in  a  cell  containing  a  nearly  saturated  and 
slightly  acidulated  solution  of  sulphate  of  copper,  and 
passing  a  current  of  a  battery  through  the  cell,  the  mould 
metallized  on  its  surface  being  the  kathode,  a  plate  of 
copper  being  employed  as  an  anode,  dissolving  gradually 
into  the  liquid  at  a  rate  exactly  equal  to  the  rate  of 
deposition  at  the  kathode.  This  use  of  a  separate  cell  or 
"  bath "  is  more  convenient  than  producing  the  electro- 
types in  the  actual  cell  of  a  Darnell's  battery.  The 
process  is  largely  employed  at  the  present  day  to  repro- 
duce repousse  and  chased  ornament  and  other  works  of 
art  in  facsimile,  and  to  multiply  copies  of  wood  blocks  for 
printing.  Almost  all  the  illustrations  in  this  book,  for 
example,  are  printed  from  electrotype  copies,  and  not 
from  the  original  wood  blocks,  which  would  not  wear  so 
wTell.  In  all  deposition  processes  success  largely  depends 
on  having  the  proper  current-density.  To  deposit  metals 
that  are  more  positive  than  hydrogen,  such  as  zinc  or 
chromium,  it  is  advisable  to  use  concentrated  solutions 
and  high  current-densities.  For  metals  that  are  less 
positive,  such  as  copper  and  silver,  the  current-density 
may  be  less.  To  procure  a  good  tough  deposit  of  copper 
the  current  should  not  exceed  15  amperes  per  square  foot 
of  kathode  surface.  If  a  more  rapid  deposit  is  required, 
a  solution  of  nitrate  of  copper  should  be  used  and  kept  in 
rapid  agitation. 

To  deposit  iron  (by  the  process  known  as  acierage,  or 
steel-facing")  a  very  large  sheet  of  iron  is  used  as  anode, 
and  the  liquid  used  is  simply  a  solution  of  sal  ammoniac 
in  water.  This  solution  is  "  charged "  with  iron  by 
passing  the  current  for  a  little  time  through  the  bath 
prior  to  inserting  the  object  to  be  steel-faced. 

496.  Electroplating.  —  In  1801  Wollaston  observed 
that  a  piece  of  silver,  connected  with  a  more  positive 
metal,  became  coated  with  copper  when  put  into  a  solu- 
tion of  copper.  In  1805  Brugnatelli  gilded  two  silver 


CHAP.    XI 


ELECTROPLATING 


523 


medals  by  making  them  the  kathodes  of  a  cell  containing 
a  solution  of  gold.  Messrs.  Elkington,  about  the  year 
1840,  introduced  the  commercial  processes  of  electro- 
plating. In  these  processes  a  baser  metal,  such  as  German 
silver  (an  alloy  of  zinc,  copper,  and  nickel),  is  covered 
with  a  thin  film  of  silver  or  gold,  the  solutions  employed 
being,  for  electro-gilding,  the  double  cyanide  of  gold  and 
potassium,  and  for  electro-silvering  the  double  cyanide  of 
silver  and  potassium. 

Fig.  269  shows  a  battery  and  a  plating-vat  containing 
the  silver  solution.     As  anode  is  hung  a  plate  of  metallic 


silver  which  dissolves  into  the  liquid.  To  the  kathode 
are  suspended  the  spoons,  forks,  or  other  articles  which 
are  to  receive  a  coating  of  silver.  The  addition  of  a 
minute  trace  of  bisulphide  of  carbon  to  the  solution 
causes  the  deposited  metal  to  have  a  bright  surface.  If 
the  current  is  too  strong,  and  the  deposition  too  rapid, 
the  deposited  metal  is  grayish  and  crystalline. 

In  gilding  base  metals,  such  as  pewter,  they  are 
usually  first  copper-coated.  The  gilding  of  the  insides  of 
jugs  and  cups  is  effected  by  filling  the  jug  or  cup  with  the 
gilding  solution,  and  suspending  in  it  an  anode  of  gold, 


624  ELECTRICITY  AND   MAGNETISM      PART  n 

the  vessel  itself  being  connected  to  the  —  pole  of  the 
battery. 

In  silvering  or  gilding  objects  of  iron  it  is  usual  first 
to  plate  them  with  a  thin  coating  of  copper  deposited 
from  an  "  alkaline  "  copper  bath  containing  an  ammonia- 
cal  solution  of  cyanide  of  copper.  Brass  is  deposited  also 
from  an  ammoniacal  solution  of  the  mixed  cyanides  of 
copper  and  zinc.  In  the  deposition  of  nickel  a  solution 
of  the  double  sulphate  of  nickel  and  ammonium  is  used ; 
the  anode  being  a  sheet  of  rolled  (or  cast)  nickel. 

Except  on  the  very  small  scale  batteries  are  now 
seldom  used  for  electro  typing  and  plating.  A  shunt- 
wound  dynamo  designed  to  give  a  large  output  of  current 
at  5  to  10  volts  pressure  is  generally  preferred. 

496a.  Other  Electrolytic  Processes.  —  The  electro- 
lytic action  of  the  current  is  now  commercially  employed 
for  other  purposes  than  the  deposition  of  metals.  By  the 
electrolysis  of  chloride  of  potassium  under  suitable  con- 
ditions chlorate  of  potash  is  now  manufactured  in  large 
quantities.  Bleaching  liquors  containing  hypochlorites 
can  also  be  produced  from  chlorides.  Caustic  soda  is 
prepared  by  electrolysis  of  common  salt;  and  several 
electrolytic  methods  of  disinfecting  sewage  have  been 
proposed. 

It  has  also  been  shown  that  the  slow  processes  of  tan- 
ning can  be  accelerated  by  the  aid  of  electric  currents,  the 
action  being  probably  osmotic  rather  than  electrolytic. 

It  seems  probable  that  in  the  future  the  use  of  electric 
currents  will  enter  largely  into  the  chemical  manufactures. 


CHAPTER  XII 

TELEGRAPHY 

LESSON  L.  —  Electric  Telegraphs 

497.  The  Electric  Telegraph. —It  is  difficult  to 
assign-  the  invention  of  the  telegraph  to  any  particular 
inventor.  Lesage  (Geneva,  1774),  Lomond  (Paris,  1787), 
and  Sir  F.  Ronalds  (London,  1816)  invented  systems  for 
transmitting  signals  through  wires  by  observiiig  at  one 
end  the  divergence  of  a  pair  of  pith-balls  when  a  charge 
of  electricity  wras  sent  into  the  other  end.  Cavallo 
(London,  1795)  transmitted  sparks  from  Leyden  jars 
through  wires  "  according  to  a  settled  plan."  Soemmering 
(Munich,  1808)  established  a  telegraph  in  which  the 
signals  were  made  by  the  decomposition  of  water  in  volta- 
meters ;  and  the  transmission  of  signals  by  the  chemical 
decomposition  of  substances  was  attempted  by  Coxe,  R. 
Smith,  Bain,  and  others.  Ampere  (Paris,  1821)  suggested 
that  a  galvanometer  placed  at  a  distant  point  of  a  circuit 
might  serve  for  the  transmission  of  signals.  Schilling 
and  Weber  (Gb'ttingen,  1833)  employed  the  deflexions  of 
a  galvanometer  needle  moving  to  right  or  left  to  signal  an 
alphabetic  code  of  letters  upon  a  single  circuit.  Cooke 
and  Wheatstone  (London,  1837)  brought  into  practical 
application  the  first  form  of  their  needle  telegraph.  Henry 
(New  York,  1831)  utilized  the  attraction  of  an  electro- 
magnet to  transmit  signals,  the  movement  of  the  armature 
525 


526  ELECTRICITY   AND   MAGNETISM      PART  11 

producing  audible  sounds  according  to  a  certain  code. 
Morse  (New  York,  1837)  devised  a  telegraph  in  which 
the  attraction  of  an  armature  by  an  electromagnet  was 
made  to  mark  a  dot  or  a  dash  upon  a  moving  strip  of 
paper.  Steinheil  (Munich,  1837)  discovered  that  instead 
of  a  return-wire  the  earth  might  be  used,  contact  being- 
made  to  earth  at  the  two  ends  by  means  of  earth-plates 
(see  Fig.  274)  sunk  in  the  ground.  Gintl  (1853)  and 
Stearns  (New  York,  1870)  devised  methods  of  duplex 
signalling.  Stark  (Vienna)  and  Bosscha  (Leyden,  1855) 
invented  diplex  signalling,  and  Heaviside  (London,  1873) 
and  Edison  (Newark,  N.  J.,  1874)  invented  quadruplex 
telegraphy.  Varley  (London,  1870)  and  Elisha  Gray 
(Chicago,  1874)  devised  harmonic  telegraphs.  For  fast- 
speed  work  Wheatstone  devised  his  automatic  transmitter, 
in  which  the  signs  which  represent  the  letters  ar,e  first 
punched  by  machinery  on  strips  of  paper;  these  are  then 
run  at  a  great  speed  through  the  transmitting  instrument, 
which  telegraphs  them  off  at  a  much  greater  rate  than  if 
the  separate  signals  were  telegraphed  by  hand.  Hughes 
devised  a  type-printing  telegraph.  Wheatstone  invented 
an  ABC  telegraph  in  which  signals  are  spelled  by  a  hand 
which  moves  over  a  dial.  Cowper  (1876)  and  Elisha 
Gray  (1893)  invented  autographic  writing  telegraphs. 
For  cable-working  Lord  Kelvin  invented  his  mirror 
galvanometer  and  his  delicate  siphon-recorder.  It  is 
impossible  in  these  Lessons  to  describe  more  than  one  or 
two  of  the  simple  ordinary  forms  of  telegraph  instrument 
now  in  use  in  Great  Britain.  Students  desiring  further 
information  should  consult  the  excellent  manuals  on 
Telegraphy  by  Messrs.  Preece  and  Sive Wright,  and  by 
Mr.  Culley. 

498.  Single-Needle  Instrument.  —  The  single-needle 
instrument  (Fig.  270)  consists  essentially  of  a  vertical 
galvanometer,  in  which  a  lightly  hung  magnetic  needle 
is  deflected  to  right  or  left  when  a  current  is  sent,  in 
one  direction  or  the  other,  around  a  coil  surrounding 


>.  xii      SINGLE-NEEDLE   TELEGRAPH 


527 


the  needle ;  the  needle  visible  in  front  of  the  dial  is  but 
an  index,  the  real  magnetic  needle  being  behind.  A  code 
of  movements  agreed  upon 
comprises  the  whole  alphabet 
in  combinations  of  motions 
to  right  or  left.  In  order  to 
send  currents  in  either  direc- 
tion through  the  circuit,  a 
"  signalling  key "  or  ';  tap- 
per" is  usually  employed. 
The  tapper  at  one  end  of 
the  line  works  the  instru- 
ment at  the  other;  but  for 
the  sake  of  convenience  it 
is  fixed  to  the  receiving  in- 
strument. In  Fig.  270  the 
two  protruding  levers  at  the 
base  form  the  tapper,  and 
by  depressing  the  right  hand  one  or  the  left  hand  one, 
currents  are  sent  in  either  direction  at  will. 

The  principle  of  action  will  be  made  more  clear  by 


Fig.  270. 


reference  to  Fig.  271,  which  shows  a  separate  signalling 
key.  The  two  horizontal  levers  are  respectively  in  com- 
munication with  the  "line.''  and  with  the  return-line 


528  ELECTRICITY   AND   MAGNETISM      PART  n 

through  "earth."  When  not  in  use  both  levers  spring 
up  against  a  cross  strip  of  metal  joined  to  the  zinc  pole 
of  the  battery.  At  their  further  end  is  another  cross 
strip,  which  communicates  with  the  copper  (or  +)  pole 
of  the  battery.  On  depressing  the  "line"  key  the 
current  runs  through  the  line  and  back  by  earth,  or  in 
the  positive  direction.  On  depressing  the  "  earth  "  key 
(the  line-key  remaining  in  contact  with  the  zinc-connected 
strip),  the  current  runs  through  the  earth  and  back  by 
the  line,  or  in  the  negative  direction.  Telegraphists 
ordinarily  speak  of  these  as  positive  and  negative  currents 
respectively. 

499.  The  Morse  Instrument.  —  The  most  widely 
used  instrument  at  the  present  day  is  the  Morse.  It 
consists  essentially  of  an  electromagnet,  which,  when  a 
current  passes  through  its  coils,  draws  down  an  armature 
for  a  short  or  a  long  time.  It  may  either  be  arranged  as 
a  "  sounder,"  in  which  case  the  operator  who  is  receiving 
the  message  listens  to  the  clicks,  and  notices  whether  the 
intervals  between  them  are  long  or  short ;  or  it  may  be 

arranged  as  an 
"  embosser,"  to  print 
dots  and  dashes 
upon  a  strip  of 
paper  drawn  by 
clockwork  through 
the  instrument.  In 
the  most  modern 
form,  however,  the 
Morse  instrument 
is  arranged  as  an 
"  ink -writer  "  in 

which  the  attraction  of  the  armature  downwards  lifts  a 
little  inky  wheel  and  pushes  it  against  a  ribbon  of  paper. 
The  Morse  Sounder,  which  is  almost  universal  in  the 
United  States,  and  is  being  increasingly  used  in  the 
British  Telegraph  Service,  is  depicted  in  Fig.  272.  In 


CHAP.    XII 


MORSE   INSTRUMENT 


529 


this  instrument  the  electromagnet  is  of  inverted  horse- 
shoe pattern,  having  the  coils  wound  on  two  bobbins 
which  are  slipped  over  vertical  cores.  Above  the  poles  lies 
an  iron  armature  fixed  across  the  pivoted  lever.  When- 
ever the  current  passes  through  the  coils  the  armature  is 
attracted  down,  and  the  lever  makes  a  click  as  it  strikes 
against  a  stop.  As  soon  as  the  current  ceases  the  lever  is 
raised  by  a  spring  and  strikes  against  a  top  stop.  There 
are  therefore  two  clicks  heard.  When  "a  "  dot "  is  sig- 
nalled the  two  clicks  are  heard  immediately  after  one 
another.  When  a  "  dash  **  is  signalled  the  interval  be- 
tween the  clicks  is  longer.  With  a  little  practice  it 
becomes  easy  to  read  the  sounder. 

The  Morse  Ink- Writer,  as  used  in  the  British  Postal 
Telegraph  Service,  is  depicted  in  Fig.  273.  A  piece  of 
clockwork  causes  a  ribbon  of  paper  (coiled  up  in  the 

LOCAL  BATTERY 


EARTH 


SENDING   BATTERY 

Jfig.  27-3. 


base  of  the  instrument)  to  be  slowly  drawn  between 
rollers,  while  the  dots  and  dashes  are  printed  on  it  by 
the  ink-wheel  affixed  to  the  end  of  the  lever,  A  moinen- 


530  ELECTRICITY   AND   MAGNETISM      PART  n 

tary  current  prints  a  mere  dot ;  but  if  the  current  con- 
tinues to  flow  for  a  longer  time  while  the  ribbon  of  paper 
moves  on,  the  ink-wheel  records  a  dash.  The  connexions 
show  how  the  instrument  is  worked  by  a  local  battery 
and  a  relay. 

499a.  The  Morse  Alphabets.  —  The  international 
Morse  code,  or  alphabet  of  dots  and  dashes,  is  as 
follows :  — 

A.—  "j.___     S... 

B    —  .  .  .  K    —  .  -  T 

C    —  .  —  .        L    .—  .  .  U    ..— 

D   —  .  .  M  -  V    .  .  .  - 

E    .  N   —  .  W  .  - 

F    .  .  —  .  O    -  X 

G .          P    . .        Y    --.- 

H....  Q-      -.-      Z          -.. 

I     .  .  11    .  —  . 

The  American  Morse  code,  originated  by  Morse  himself,  is 
used  only  in  the  United  States  and  Canada.  It  differs  in  many 
respects  from  the  International  code,  the  signals  for  some  of  the 
letters  depending  on  the  length  of  the  spadngs  between  the  dots 
and  dashes ;  and  more  than  four  marks  are  used  to  form  some 
of  the  letters.  The  marks  for  H,  Y,  and  Z  are  four  dots,  but 
they  are  differently  spaced.  The  following  is  the  American 
Morse  code :  — 

A    .  _  M Y    .  .   .  . 

B    _...  N   —  .  Z    .   ... 

C    ..   .  O    .   .  1     • 

D   —  .  .  P    2..  —  .. 

E    .  Q    ..  — .  3     .  .  .  — . 

F    .  —  .  R    .   .  .  4     .  .  .  .  - 

G .  S     ...  5 

II T  6     

I     .  .  U    .  .  -  7 

J     -.  — .  V    .  .  .-  8    — 

K   —  .  —  W  .  —  -  9      -  .  .  - 

L    X   .-..  0 


CHAP,  xii  MORSE   KEY  531 

499b.  The  Morse  Key.  —  The  key  used  for  operat- 
ing Morse  telegraphs.  The  American  pattern  differ? 
somewhat  from  the  European  pattern,  and  the  mode  of 
use  is  not  precisely  the  same. 

The  general  appearance  of  the  American  pattern  of 
Morse  key  is  shown  in  Fig.  274. 


Fig.  274. 

The  key  is  fastened  to  the  table  by  the  screws  B  and 
L,  the  former  being  insulated  from  the  metal  base  and 
lever,  while  L  is  not  insulated.  One  wire  is  clamped 
to  the  metal  of  the  key  at  L,  the  other  is  clamped  to  B. 
The  lever,  which  is  provided  with  a  finger-piece,  has  on 
its  lower  side  a  short  platinum  pin  just  above  the  head 
of  the  screw  B,  so  that  when  the  operator  depresses  the 
lever  it  makes  contact  on  the  head  of  the  screw  and  com- 
pletes the  circuit  from  B  to  L.  The  range  of  motion 
allowed  the  lever  is  regulated  by  a  screw-stop  in  the 
further  end  of  the  lever.  Beside  the  parts  named  the  key 
is  usually  provided  with  a  switch,  shown  in  the  Fig.  274 
with  a  small  vertical  handle.  When  this  is  moved  to  the 
left  it  short-circuits  the  key,  and  puts  B  into  direct  con- 
nexion with  L.  When  moved  to  the  right,  the  circuit  is 
open  until  such  time  as  the  lever  is  depressed. 

The  Morse  key  as  used  in  the  British  telegraphs  is 


532  ELECTRICITY   AND   MAGNETISM      PART  n 

depicted  in  Fig.  275.     The  line  wire  is  connected  with 

the  central  pivot  A. 
A  spring  keeps  the 
front  end  of  the  key 
elevated  when  not 
in  use,  so  that  the 
line  wire  is  in  com- 
i  rumication  through 
the  rear  end  of  the 
key  with  the  receiv- 
ing. ii7f».  ing  instrument  or 
relay.  Depressing 

the  key  breaks  this  communication,  arid  by  putting  the 
line  wire  in  communication  with  the  sending  battery 
transmits  a  current  through  the  line. 

5OO.  Open  and  Closed  Circuit  Working.  —  European 
telegraphs  work  on  the  open-circuit  plan,  the  battery  being 
out  of  circuit  when  no  message  is  being  sent.  American 
telegraphs  are  usually  on  the  closed-circuit  plan,  the 
current  being  always  on  until  interrupted  to  send  signals. 
Each  plan  has  its  advantages.  The  closed-circuit  plan 
enables  a  way-line  to  unite  a  number  of  isolated  stations 
all  in  a  single  circuit,  each  one  of  which  can  signal  to  all 
the  re^t  by  opening  the  circuit.  Further,  any  failure  in 
the  line  immediately  reports  itself  by  the  stoppage  of  the 
current.  The  open-circuit  plan,  which  is  better  suited 
for  communication  among  dense  populations,  and  for  all 
lines  where  no  instruments  are  wanted  to  be  inserted  at 
intermediate  points,  has  the  advantage  of  only  using  the 
batteries  when  the  telegraph  is  in  actual  use. 

In  the  open-circuit  plan  the  key  acts,  as  previously 
described,  merely  to  open  or  close  the  circuit.  The 
general  arrangement  of  apparatus  at  an  intermediate  or 
"way"  station  is  shown  in  Fig.  270.  The  current  com- 
ing along  the  line  enters  by  the  line  wire  on  the  right 
and  comes  in  to  the  metal  base  of  the  key  K,  where  it 
finds  a  passage  along  the  switch  G  (which  is  closed)  to 


CHAP.     XII 


OPEN-CIRCUIT   METHOD 


538 


the  head  H  of  the  screw  (described  as  screw  B  of  Fig. 
274).  Thence  it  passes  to  the  relay  II,  entering  it  at  the 
terminal  A,  passing  around  the  electromagnet  M  of  the 
relay ;  and  issuing  by  the  terminal  B  it  passes  down 


LINE 


Fig.  276. 


the  line  to  the  next  station.  This  current  is  furnished 
either  by  a  single  battery  inserted  in  the  line,  or  by  two 
batteries,  one  at  each  end  of  the  line  acting  in  the  same 
direction.  The  action  of  the  relay  is  considered  below. 
In  the  open-circuit  method,  as  it  is  necessary  that  a 
line  should  be  capable  of  being  worked  from  either  end, 
a  battery  is  used  at  each,  and  the  wires  so  connected  that 
when  at  either  end  a  message  is  being  received,  the 
battery  circuit  at  that  end  shall  be  open.  Fig.  277  shows 
the  simplest  possible  case  of  such  an  arrangement.  At 
each  end  is  a  battery  zc,  one  pole  of  which  is  put  to  earth, 
and  the  other  communicates  with  the  middle  point  of  a 
Morse  key  K.  This  key  is  arranged  (like  that  in  Fig. 
275)  so  that  when  it  is  depressed  to  send  a  signal  through 
the  line  it  quits  contact  with  the  receiving  instrument  at 


534 


ELECTRICITY   AND    MAGNETISM      PART  n 


its  own  end.  Both  ends  of  the  lever  must  therefore  be 
furnished  with  contact-pins  of  platinum;  and  the  key 
acts  as  a  two-way  key.  The  current  flowing  through  the 


Fig.  277. 

line  passes  through  K'  and  enters  a  receiving  instrument 
G'  at  the  distant  end,  where  it  produces  a  signal,  and 
returns  by  the  eartli  to  the  battery  whence  it  started.  A 
similar  battery  and  key  at  the  distant  end  suffice  to  trans- 
mit signals  in  the  opposite  direction  to  G  when  K  is  not 
depressed.  The  diagram  is  drawn  as  if  G  were  a  simple 
galvanometer ;  but  the  arrangement  would  perfectly  suit 
the  Morse  instrument,  in  which  it  is  only  required  at 
either  end  to  send  long  and  short  currents  without  revers- 
ing the  direction,  as  with  the  needle  instruments.  In 
this  diagram  the  battery  current  is  never  reversed 
and  the  method  is  known  as  a  single-current  method. 
There  is  a  so-called  double-current  method  of  working,  in 
which  reversing  keys  (resembling  the  tapper  of  Fig. 
271)  are  used  to  send  after  each  current  in  the  positive 
direction  a  second  current  in  the  negative  direction.  The 
double-current  method  has  the  advantage  of  enabling 


CHAP,  xii  RELAYS 


the  signalling  to  bo  more  rapid  on  long  lines  when  the 
retardation  due  to  the  static  charging  of  the  line  is  of 
importance.  The  second  current  helps  to  curb  the  first 
and  makes  the  signals  shorter  and  sharper. 

5O1.  Relays.  —  In  working  over  long  lines,  or  where 
there  are  a  number  of  instruments  on  one  circuit,  the 
currents  are  often  not  strong  enough  to  work  the  record- 
ing instrument  directly.  In  such  a  case  there  is  inter- 
posed a  relay  or  repeater.  This  instrument  consists  of 
an  electromagnet  round  which  the  line  current  flows,  and 
whose  delicately  poised  armature,  when  attracted,  makes 
contact  for  a  local  circuit  in  which  a  local  battery  and 
the  receiving  Morse  instrument  (sounder,  or  writer)  are 
included.  The  principle  of  the  relay  is,  then,  that  a  cur- 
rent too  weak  to  do  the  work  itself  may  set  a  strong  local 
current  to  do  its  work  for  it. 

In  the  American  plan  of  working  (Fig.  276),  the  relay 
is  a  simple  electromagnet  having  a  soft-iron  core,  and  an 
armature  of  iron  which  it  attracts  whenever  a  current 
flows  round  its  coils.  It  pulls  its  armature  no  matter 
which  way  the  current  flows.  Such  a  non-polarized 
relay  of  the  Western  Union  pattern  is  depicted  in  Fig. 


Fig.  278. 

278.  Its  mode  of  operation  is  explained  by  the  dia- 
grammatic plan  of  Fig.  276.  Here  M  is  the  electromag- 
net, with  its  iron  armature  lightly  pivoted  at  P,  and 
controlled  by  the  spring  V.  When  any  current  passes,  the 


536  ELECTRICITY   AND   MAGNETISM      PART  n 

light  lever  or  tongue  on  which  the  armature  is  mounted 
turns  on  its  pivot  P,  and  makes  contact  against  the  stop  D, 
thereby  closing  a  local  circuit  DXLSYP,  which  includes 
the  sounder  S  and  a  local  battery  L. 

In  the  closed-circuit  method  of  working,  and  in 
duplex  telegraphy  "polarized  relays"  are  used,  which 
will  respond  to  currents  flowing  in  one  direction  only. 
The  polarized  relay  of  Siemeus's  pattern  is  shown  in 
diagram  in  Fig.  279.  In  it  a  permanently  magnetized 
steel  magnet  is  employed  to  produce  an  initial  magnetism 
in  the  cores  of  the  electromagnet,  and  in  the  pivoted 
lever  or  tongue.  The  magnet  lias  its  S  pole  bent  up  at 


9  TO  LINE 


"  I 

TO  LOCAL 


N°OER 


Fig.  279. 

right  angles  and  divided  so  that  the  tongue  aD  of  the 
relay,  which  is  of  iron,  may  be  thereby  polarized  or 
given  a  south  polarity.  Attached  to  the  N"  pole  of  the 
magnet  are  the  two  cores,  over  which  the  two  bobbins 
are  slipped,  these  cores  ending  in  the  two  pole-pieces 
marked  n,  n',  which  are  of  northern  polarity.  They  both 
attract  the  tongue  that  lies  between  them,  the  nearer  one 
pulling  more  strongly.  If  now  a  current  circulates  round 
the  coils  it  will  tend  to  strengthen  one  of  the  poles  and 
weaken  the  other.  If  it  flows  in  such  a  direction  as  to 
strengthen  n  and  weaken  n',  the  tongue  will  be  attracted 


CHAP.    XII 


RELAYS 


537 


over  and  will  make  contact  against  the  stop  which  is  in 
connexion  with  the  local  battery,  and  so  will  work  the 
sounder.  If  the  current  flows  in  the  opposite  sense,  so 
as  to  weaken  n  and  strengthen  n',  the  tongue  will  tend  to 
move  the  other  way  and  will  make  no  signal.  Even 
when  there  is  no  current  the  tongue  returns  back,  being- 
attracted  to  the  nearer  pole-piece.  No  springs  are 
necessary. 

The  sensitive  form  of  polarized  relay  adopted  in  the 
British  Postal  Telegraphs,  is  shown  in.  Fig.  280.  Here  the 
tongue  of  the  relay  is  fixed 
on  a  vertical  spindle,  piv- 
oted in  jewelled  holes, 
which  has  two  short  iron 
projections  upon  it.  This 
spindle  is  polarized  by  a 
powerful  steel  magnet  of 
compact  shape.  The  two 
projections  lie  between  a 
pair  of  upper  and  a  pair 
of  lower  pole-pieces  upon 
the  two  vertical  iron  cores 
of  the  electromagnets. 
These  are  wound  with  coils 
of  exceedingly  fine  silk- 
covered  wire.  The  con- 
nexions are  indicated  in  Fig.  273  where  the  tongue  of  the 
relay  is  shown  to  make  circuit,  when  it  touches  the  stop, 
for  a  local  battery  and  the  Morse  ink-writer.  Whenever 
a  current  comes  in  the  right  direction  in  the  line  it  causes 
the  tongue  of  the  relay  to  close  the  local  circuit,  and 
causes  the  Morse  to  record  either  a  dot  or  a  dash  on  the 
strip  of  paper. 

5O2.  Faults  in  Telegraph  Lines.  —  Faults  may  occur 
in  telegraph  lines  from  several  causes ;  either  from  the 
breakage  of  the  wires  or  conductors,  or  from  the  break- 
age of  the  insulators,  thereby  short-circuiting  the  current 


Fig.  2! 


538  ELECTRICITY   AND   MAGNETISM      PART  n 

through  the  earth  before  it  reaches  the  distant  station, 
or,  as  in  overhead  wires,  by  two  conducting  wires  touch- 
ing one  another.  Various  modes  for  testing  the  existence 
and  position  of  faults  are  known  to  telegraph  engineers; 
they  depend  upon  accurate  measurements  of  resistance  or 
of  capacity.  Thus,  if  a  telegraph  cable  part  in  mid-ocean 
it  is  possible  to  calculate  the  distance  from  the  shore  end 
to  the  broken  end  by  comparing  the  resistance  that  the 
cable  is  known  to  offer  per  mile  with  the  resistance 
offered  by  the  length  up  to  the  fault,  and  dividing  the 
latter  by  the  former. 

503.  Duplex  and  Quadruplex  Telegraphy.  —  To  send 
two  messages  through  one  wire,  one  from  each  end,  at 
the  same  time,  is  known  as  duplex  working.  There  are 
two  distinct  methods  of  arranging  apparatus  for  duplex 
working.  The  first  of  these,  known  as  the  differential 
method,  involves  the  use  of  instruments  wound  with  dif- 
ferential coils,  and  is  applicable  to  special  cases.  The 
second  method  of  duplex  working,  known  as  the  brulye 
method,  is  capable  of  much  more  general  application.  The 
diagram  of  Fig.  281  will  explain  the  general  principle. 
The  first  requirement  in  duplex  working  is  that  the 
instriiment  at  each  end  shall  only  move  in  response  to 
signals  from  the  other  end,  so  that  an  operator  at  R  may 
be  able  to  signal  to  the  distant  instrument  M'  without  his 
own  instrument  M  being  affected,  M  being  all  the  while 
in  circuit  and  able  to  receive  signals  from  the  distant 
operator  at  R'.  To  accomplish  this  the  circuit  is  divided 
at  R  into  two  branches,  which  go,  by  A  and  B  respectively, 
the  one  to  the  line,  the  other  through  a  certain  resistance 
P  to  the  earth.  If  the  ratio  between  the  resistances  in 
the  arms  RA  and  "RB  is  equal  to  the  ratio  of  the  resistances 
of  the  line  and  of  P,  then,  by  the  principle  of  Wheatstone's 
Bridge,  no  current  will  pass  through  M.  So  M  does  not 
show  any  currents  sent  from  R;  but  M'  will  show  them, 
for  the  current  on  arriving  at  C  will  divide  into  two 
parts,  part  flowing  round  to  the  earth  by  R',  the  other 


CHAP,  xii  DUPLEX   TELEGRAPHY  539 


part  flowing  through  M'  and  producing  a  signal.  If, 
while  this  is  going  on,  the  operator  at  the  distant  R' 
depresses  his  key  and  sends  an  equal  current  in  the 


Fig.  281. 

opposite  direction,  the  flow  through  the  line  will  cease ; 
but  M  will  now  show  a  signal,  because,  although  no 
current  flows  through  the  line,  the  current  in  the  branch 
RA  will  now  flow  down  through  M,  as  if  it  had  come 
from  the  distant  R',  so,  whether  the  operator  at  R  be 
signalling  or  not,  M  will  respond  to  signals  sent  from  R'. 
In  duplexing  long  lines  and  cables  condensers  are  em- 
ployed in  the  arms  RA  and  RB  of  the  bridge ;  and 
instead  of  a  mere  balancing  resistance  at  P  and  Q  there 
is  used  an  "  artificial  cable,"  a  combination  of  condensers 
and  resistances  to  imitate  the  electrical  properties  of  the 
actual  line  or  cable  between  the  stations. 

The  Diplex  method  of  working  consists  in  sending 
two  messages  at  once  through  a  wire  in  the  same  direc- 
tion. To  do  this  it  is  needful  to  employ  one  set  of  instru- 
ments which  works  only  with  currents  in  one  given 
direction,  and  a  second  set  which  works  only  when  the 
current,  in  either  direction*,  exceeds  a  certain  strength. 
The  method  involves  the  use  of  polarized  relays,  which, 
being  themselves  permanently  magnetized,  respond  there- 
fore only  to  currents  in  one  direction,  and  of  set-up  non- 
polarized relays  which  will  not  respond  to  currents  below 
a  certain  minimum.  Two  keys  are  used ;  one  reversing 
the  current  and  sending  it  in  either  positive  or  negative 
direction,  the  other  sending  current  always  in  the  same 


540 


ELECTRICITY   AND    MAGNETISM      PAKT 


direction,  but  sometimes  weak,  sometimes  strong.     One 

key  controls  the  direction,  the  other  the  strength  of   the 

current. 

The  method  used  by  Edison  for  transmitting  is  shown 

in  Fig.  282.     In  the  position  shown  the  battery  B  has  its 

terminals  at  N  and  P ;  the 
current  passing  from  B 
through  K2  to  the  spring  S, 
and  thence  to  P.  If  the  key 
K'  is  worked,  the  currents 
flow  into  or  out  of  the  line, 
and,  if  a  polarized  relay  is 
inserted  at  the  distant  re- 
ceiving station,  it  will  work 
its  sounder  only  for  currents 
in  one  direction,  as  sent  by 
K',  no  matter  whether  these 
currents  are  strong  or  weak. 
As  shown  in  the  figure,  the 
second  battery  B',  which 

has  more  ceHs  tnatl  B,  is  on 
open  circuit.  If,  however, 
K2  be  depressed,  the  spring  S  comes  into  contact  with  the 
point  m  and  breaks  contact  with  n,  so  that  now  the  entire 
range  of  battery  is  thrown  into  operation.  Whenever 
K2  is  depressed,  therefore,  the  points  N"  and  P  retain  their 
polarity,  but  the  current  is  of  three  or  four  times  its 
original  strength.  All  contacts  are  made  by  springs 
properly  adjusted  so  that  K2  never  breaks  the  circuit  in 
producing  the  change  of  strength  of  current.  The  mes- 
sage transmitted  by  K2  is  received  on  a  non-polarized 
relay,  the  tongue  of  which  is  controlled  by  a  spring  so 
adjusted  that  the  weak  currents  of  battery  B  will  not 
cause  the  electromagnets  to  pull  over  the  armature  ;  but 
when  K2  is  worked,  the  current  due  to  B  -f  B'  easily  pulls 
the  armature  over. 

The    Quadruplex    method   of  working   combines   the 


CHAP,  xii  SUBMARINE   CABLES  541 

duplex  and  the  diplex  methods.  On  one  and  the  same 
line  are  used  two  sets  of  receiving  instruments,  one  of 
which  (worked  by  a  polarized  relay)  works  only  when 
Hie  direction  of  the  current  is  changed,  the  other  of  which 
(worked  by  a  non-polarized  relay  adjusted  with  springs 
to  move  only  with  a  certain  minimum  force)  works  only 
when  the  strength  of  the  current  is  changed  and  is  inde- 
pendent of  their  direction.  If  in  Fig.  281,  the  diplex 
transmitting  apparatus  just  described  were  inserted  at 
each  end  instead  of  the  two  keys  R  and  R',  and  if  between 
A  ami  B  were  placed  in  series  the  two  relays,  the  figure 
would  represent  the  general  arrangement  of  the  quadru- 
ple! system  as  used  widely  in  the  United  States. 


LESSON  LI.  —  Cable  Telegraphy 

5O4.  Submarine  Cables.  —  Telegraphic  communica- 
tion between  two  countries  separated  by  a  strait  or  ocean 
is  carried  on  through  cables  sunk  to  the  bottom  of  the 


Fig.  2S3.  Fig.  284. 

sea,  which  carry  conducting  wires  carefully  protected  by 
an  outer  sheath  of  insulating  and  protecting  materials. 
The  conductor  is  usually  of  purest  copper  wire,  weighing 
from  70  to  400  Ibs.  per  nautical  mile,  made  in  a  seven- 
fold strand  to  lessen  risk  of  breaking.  Figs.  283  and 
284  show,  in  their  natural  size,  sections  of  the  Atlantic 


542  ELECTRICITY   AND   MAGNETISM      PART  11 

cables  laid  in  1857  and  1866  respectively.  In  the  latter 
cable,  which  is  of  the  usual  type  of  cable  for  long  lines, 
the  core  is  protected  first  by  a  stout  layer  of  guttapercha, 
then  by  a  woven  coating  of  jute,  and  outside  all  an 
external  sheath  made  of  ten  iron  wires,  each  covered 
with  hemp.  The  shore  ends  are  even  more  strongly  pro- 
tected by  external  wires. 

5O5.  Speed  of  Signalling  through  Cables.  —  Signals 
transmitted  through  long  cables  are  retarded,  the  re- 
tardation being  due  to  two  causes. 

Firstly,  The  self-induction  of  the  circuit  prevents  the 
current  from  rising  at  once  to  its  height,  the  retardation 
being  expressed  by  Helmholtz's  equation  (Art.  460). 

Secondly,  The  cable  in  its  insulating  sheath,  when 
immersed  in  water,  acts  laterally  like  a  Leyden  jar  of 
enormous  capacity  (as  explained  in  Art.  274),  and  the 
first  portions  of  the  current,  instead  of  flowing  through, 
remain  in  the  cable  as  an  electrostatic  charge  on  the  sur- 
face of  the  guttapercha.  For  every  separate  signal  the 
cable  must  be  at  least  partially  charged  and  then  dis- 
charged. Culley  states  that  when  a  current  is  sent 
through  an  Atlantic  cable  from  Ireland  to  Newfoundland 
no  effect  is  produced  on  the  most  delicate  instrument  at 
the  receiving  end  for  two-tenths  of  a  second,  and  that  it 
requires  three  seconds  for  the  current  to  gain  its  full 
strength,  rising  in  an  electric  wave  which  travels  forward 
through  the  cable.  The  strength  of  the  current  falls 
gradually  also  when  the  circuit  is  broken.  The  greater 
part  of  this  retardation  is  due  to  electrostatic  charge,  not 
to  electromagnetic  self-induction.  The  time  required  to 
transmit  a  given  number  of  signals  varies  in  proportion 
both  to  K  the  capacity  and  R  the  resistance  of  the  cable : 
it  is  therefore  proportional  to  KR,  and  as  each  of  these 
quantities  is  proportional  to  the  length  of  the  cable,  it 
follows  that  the  retardation  is  proportional  to  the  square 
of  the  length  of  the  cable.  The  various  means  adopted 
to  get  rid  of  this  retardation  are  explained  in  Art.  323. 


CHAP,  xii         MULTIPLEX   TELEGRAPHS  543 

It  is  usual  to  insert  in  the  circuit  at  each  end  of  the  cable 
a  condenser  of  several  microfarads,  through  which  the  sig- 
nals pass.  The  tendency  of  the  condenser  to  discharge 
helps  to  curb  the  signals  and  make  each  shorter  and 
sharper.  It  is  theoretically  possible  (compare  Art.  438) 
to  compensate  capacity  by  self-induction;  but  as  the 
capacity  of  a  cable  is  lateral,  not  longitudinal,  and  dis- 
tributed all  along  it,  the  self-induction  coils  to  compen- 
sate the  retardation  would  have  to  be  applied  as  shunts 
at  intervals.  A  cable  with  a  self-inductive  shunt  or  leak 
at  a  point  near  its  middle  transmits  signals  more  rapidly 
than  one  not  so  compensated. 

5O6.  Receiving  Instruments  for  Cables.  —  The  mirror- 
galvanometer  of  Lord  Kelvin  (Art.  215)  was  devised 
for  cable  signalling,  the  movements  of  the  spot  of  light 
sweeping  over  the  scale  to  a  short  or  a  long  distance 
sufficing  to  signal  the  dots  and  dashes  of  the  Morse 
code.  Lord  Kelvin's  Siphon  Recorder  is  an  instrument 
which  writes  the  signals  upon  a  strip  of  paper  by  the 
following  ingenious  means:  —  The  cable  communicates 
with  a  delicately-suspended  coil  of  wire  that  hangs  be- 
tween the  poles  of  a  powerful  magnet.  To  the  suspended 
coil  is  attached  a  fine  siphon  of  glass  suspended  by  a  silk 
fibre,  one  end  of  which  dips  into  an  ink  vessel.  The  ink 
makes  marks  upon  a  strip  of  paper  (moved  by  clockwork 
vertically  past  the  siphon),  friction  being  obviated  by 
giving  the  siphon  a  continual  minute  vibration.  The 
siphon  record  is  a  wavy  line  having  short  and  long  waves 
for  dots  and  dashes. 


LESSON  LIT.  —  Miscellaneous  Telegraphs 

5O7.  Multiplex  Telegraphs.  —  Varley  proposed  to 
send  messages  by  transmitting  electrically  musical  tones, 
interrupted  to  sound  as  dots  and  dashes.  This  necessi- 
tated the  transmission  of  currents  either  rapidly  alternat- 


544  ELECTRICITY   AND    MAGNETISM      PART  n 


ing  or  rapidly  intermittent.  Gray,  who  constructed 
harmonic  telegraphs  on  this  plan,  found  it  possible  to 
transmit  five  or  six  messages  simultaneously  in  one  line. 

By  using1  at  each  end  of  a  line  two  synchronously 
revolving  distributing  switches,  it  is  possible  to  send 
several  messages  at  once  through  a  line ;  the  distributors 
(invented  by  Delany)  causing  each  transmitting  instru- 
ment to  be  in  circuit  with  its  corresponding  receiving 
instrument  for  a  small  fraction  of  a  second  at  regular 
short  intervals. 

508.  Electric  Bells.  —  The  common  form  of  Electric 
Trembling  Bell  (invented  1850  by  John  Mirand)  consists 
of  an  electromagnet,  which  moves  a  hammer  backward 
and  forward  by  alternately  attracting  and  releasing  it,  so 
that  it  beats  against  a  bell.  The  arrangements  of  the 
instrument  are  shown  in  Fig.  285,  in  which  E  is  the 
electromagnet  and  II  the  hammer.  A  battery,  consisting 
of  one  or  two  Leclanchc  cells  placed  at  some  convenient 
point  of  the  circuit,  provides  a  current  when  required. 
By  touching  the  "  push  "  P,  the  circuit  is  completed,  and 
a  current  flows  along  the  line  and  round  the  coils  of  the 
electromagnet,  which  forthwith  attracts  a  small  piece  of 
soft  iron  attached  to  the  lever,  which  terminates  in  the 
hammer  H.  The  lever  is  itself  included  in  the  circuit, 
the  current  entering  it  above  and  quitting  it  at  C  by  a 
contact-breaker,  consisting  of  a  spring  tipped  with  plat- 
inum resting  against  the  platinum  tip  of  a  screw,  from 
which  a  return  wire  passes  back  to  the  zinc  pole  of  the 
battery.  As  soon  as  the  lever  is  attracted  forward  the 
circuit  is  broken  at  C  by  the  spring  moving  away  from 
contact  with  the  screw  ;  hence  the  current  stops,  and  the 
electromagnet  ceases  to  attract  the  armature,  but  the 
momentum  of  the  hammer  carries  it  forward.  Imme- 
diately afterwards,  however,  the  hammer  falls  back,  again 
establishing  contact  at  C,  whereupon  the  armature  is  once 
more  attracted  forward,  and  so  on.  The  push  P  is  shown 
in  section  in  Fig.  286.  It  usually  consists  of  a  cylindri- 


CHAP.    XII 


ELECTRIC   CLOCKS 


545 


cal  knob  of  ivory  or  porcelain  capable  of  moving  loosely 
through  a  hole  in  a  circular  support  of  porcelain  or  wood, 
and  which,  when  pressed,  forces  a  platinum-tipped  spring 


Fig.  285. 


Fig.  286. 


against  a  metal  pin,  and  so  makes  electrical  contact  be- 
tween the  two  parts  of  the  interrupted  circuit.  Bells, 
having  a  polarized  armature,  and  without  any  break, 
are  used  as  call-bells  or  telephones ;  the  generator  being 
a  small  magneto  alternator  like  Fig.  259,  driven  by  a 
handle. 

5O9.  Electric  Clocks  and  Chronographs.  —  Clocks  may 
be  either  driven  or  controlled  by  electric  currents.  Bain, 
Hipp,  and  others  have  devised  electric  clocks  of  the  first 
kind,  in  which  the  ordinary  motive-power  of  a  weight  or 
spring  is  abandoned,  the  clock  being  driven  by  its  pen- 
dulum, the  "bob"  of  which  is  an  electromagnet  alter- 
nately attracted  from  side  to  side.  The  difficulty  of 
maintaining  a  perfectly  constant  battery  current  has 
prevented  such  clocks  from  coming  into  use. 

2N 


546  ELECTRICITY   AND   MAGNETISM      PART  n 

Electrically  controlled  clocks,  governed  by  a  standard 
central  clock,  have  proved  a  more  fruitful  invention.  In 
these  the  standard  timekeeper  is  constructed  so  as  to 
complete  a  circuit  periodically,  once  every  minute  or  half 
minute.  The  transmitted  currents  set  in  movement  the 
hands  of  a  system  of  dials  placed  at  distant  points,  by 
causing  an  electromagnet  placed  behind  each  dial  to 
attract  an  armature,  which,  acting  upon  a  ratchet  wheel 
by  a  pawl,  causes  it  to  move  forward  through  one  tooth 
at  each  specified  interval,  and  so  carries  the  hands  round 
at  the  same  rate  as  those  of  the  standard  clock. 

Electric  chronographs  are  used  for  measuring  very 
small  intervals  of  time.  A  stylus  fixed  to  the  armature 
of  an  electromagnet  traces  a  line  upon  a  piece  of  paper 
fixed  to  a  cylinder  revolving  by  clockwork.  A  current 
sent  through  the  coils  of  the  electromagnet  moves  the 
armature  and  causes  a  lateral  notch  in  the  line  so  traced. 
Two  currents  are  marked  by  two  notches ;  and  from  the 
interval  of  space  between  the  two  notches  the  interval  of 
time  which  elapsed  between  the  two  currents  may  be  cal- 
culated to  the  ten-thousandth  part  of  a  second  if  the 
speed  of  rotation  is  accurately  known.  The  velocity  with 
which  a  cannon  ball  moves  along  the  bore  of  the  cannon 
can  be  measured  thus. 


CHAPTER  XIII 

TELEPHONY 

LESSON  LIII. — Electric  Telephones 

51O.  Early  Telephones.  —  The  first  successful  attempt 
to  transmit  sounds  electrically  was  made  in  1861  by  Reis, 
who  succeeded  in  conveying  musical  and  other  tones  by 
an  imperfect  telephone.  In  this  instrument  the  voice 
was  caused  to  act  upon  a  point  of  loose  contact  in  an 
electric  circuit,  and  by  bringing  those  parts  into  greater 
or  less  intimacy  of  contact  (Art.  400),  thereby  varied  the 
resistance  offered  to  the  circuit.  The  transmitting  part 
of  Reis's  telephone  consisted  of  a  battery  and  a  contact- 
breaker,  the  latter  being  formed  of  a  tympanum  or  dia- 
phragm of  stretched  membrane,  capable  of  taking  up 
sonorous  vibrations,  and  having  attached  to  it  a  thin 
elastic  strip  of  platinum,  which,  as  it  vibrated,  beat  to 
and  fro  against  the  tip  of  a  platinum  wire,  so  making  and 
breaking  contact  wholly  or  partially  at  each  vibration  in 
exactly  the  same  manner  as  is  done  with  the  carbon 
contacts  in  the  modern  transmitters  of  Blake,  Berliner, 
etc.  The  receiving  part  of  the  instrument  consisted  of  an 
iron  wire  fixed  upon  a  sounding-board  and  surrounded 
by  a  coil  of  insulated  wire  forming  part  of  the  circuit. 
The  rapid  magnetization  and  demagnetization  of  such  an 
iron  core  will  produce  audible  sounds  (Art.  124).  If  the 
current  vary,  the  iron  wire  is  partially  magnetized  or 
547 


548  ELECTRICITY   AND   MAGNETISM      PART  11 


demagnetized,  giving  rise  to  corresponding  vibrations  of 
varying  amplitudes  and  forms;  hence  such  a  wire  will 
serve  perfectly  as  a  receiver  to  reproduce  speech  if  a  good 
transmitter  is  used.  Reis  himself  transmitted  speech 
with  his  instrument,  but  only  imperfectly,  for  all  tones  of 
speech  cannot  be  transmitted  by  abrupt  interruptions  of 
the  current,  to  which  Reis's  transmitter  is  prone  when 
spoken  into,  owing  to  the  extreme  lightness  of  the  contact : 
they  require  gentle  undulations,  sometimes  simple,  some- 
times complex,  according  to  the  nature  of  the  sound. 
The  vowel  sounds  are  produced  by  periodic  and  complex 
movements  in  the  air ;  the  consonants  being  for  the  most 
part  non-periodic.  Reis  also  devised  a  second  receiver,  in 
which  an  electromagnet  attracted  an  elastically-supported 
armature  of  iron,  which  vibrated  under  the  attraction  of 
the  more  or  less  interrupted  current. 

In  1876  Elisha  Gray  devised  a  transmitter  in  which 
a  variable  water-resistance  (made  by  a  platinum  wire 
dipping  into  water)  was  acted  upon  by  the  voice.  He 
designed  an  electromagnetic  receiver. 

Telephone  receivers  were  invented  by  Varley  and 
Dolbear,  in  which  the  attraction  between  the  oppositely- 
electrified  armatures  of  a  condenser  is  utilized  in  the  pro- 
duction of  sounds.  Dolbear's  receiver  consists  merely  of 
two  thin  metal  disks,  separated  by  a  very  thin  air-space. 
As  the  varying  currents  flow  into  and  out  of  this  con- 
denser the  two  disks  attract  one  another  more  or  less 
strongly,  and  thereby  vibrations  are  set  up  which  corre- 
spond to  the  vibrations  of  the  original  sound. 

In  1876  Graham  Bell  invented  the  magneto-telephone. 
In  this  instrument  the  speaker  talks  to  an  elastic 
plate  of  thin  sheet  iron,  which  vibrates  and  transmits 
its  every  movement  electrically  to  a  similar  plate  in 
a  similar  telephone  at  a  distant  station,  causing  it  to 
vibrate  in  an  identical  manner,  and  thereby  to  emit 
identical  sounds.  The  transmission  of  the  vibrations 
depends  upon  the  principles  of  magneto-electric  indue- 


CHAP.    XIII 


EARLY   TELEPHONES 


549 


tion  explained  in  Lesson  VIII.  Fig.  287  shows  Bell's 
Telephone  in  section.  The  disk  D  is 
placed  behind  a  conical  mouthpiece,  to 
which  the  speaker  places  his  mouth  or 
the  hearer  his  ear.  Behind  the  disk  is  a 
magnet  A  A  running  the  length  of  the 
instrument;  and  upon  its  front  pole, 
which  nearly  touches  the  disk,  is  fixed  a 
small  bobbin,  on  which  is  wound  a  coil  C 
of  fine  insulated  wire,  the  ends  of  the 
coil  being  connected  with  the  terminal 
screws  FF.  One  such  instrument  is  used 
to  transmit,  and  one  to  receive  the  sounds, 
the  two  being  connected  in  simple  circuit. 
No  battery  is  needed,  for  the  transmitting 
instrument  itself  generates  the  induced  currents  as  fol- 
lows:  The  magnet  AA  induces  a  certain  number  of 
magnetic  lines  through  the  coil  C.  Many  of  these  pass 
into  the  iron  disk.  When  the  iron  disk  in  vibrating 
moves  toward  the  magnet-pole  more  magnetic  lines  meet 
it ;  when  it  recedes,  fewer  lines  meet  it.  Its  motion  to 
and  fro  will  therefore  alter  the  number  of  lines  ivhich  pass 
through  the  hollow  of  the  coil  C,  and  will  therefore  (Art.  107) 
generate  in  the  wire  of  the  coils  currents  whose  strength 
is  proportional  to  the  rate  of  change  in  the  number  of 
the  lines.  Bell's  instrument,  when  used  as  a  transmitter, 
may  therefore  be  regarded  as  a  sort  of  vibrating  dynamo, 
which  pumps  currents  in  alternate  directions  into  the 
wire.  At  the  distant  end  the  currents  as  they  arrive 
flow  round  the  coils  either  in  one  direction  or  the  other, 
and  therefore  either  add  momentarily  to  or  take  from  the 
strength  of  the  magnet.  When  the  current  in  the  coils 
is  in  such  a  direction  as  to  reinforce  the  magnet,  the 
magnet  attracts  the  iron  disk  in  front  of  it  more  strongly 
than  before.  If  the  current  is  in  the  opposite  direction 
the  disk  is  less  attracted  and  flies  back.  Hence,  whatever 
movement  is  imparted  to  the  disk  of  the  transmitting 


550  ELECTRICITY   AND    MAGNETISM      PART  11 

telephone,  the  disk  of  the  distant  receiving  telephone  is 
forced  to  repeat,  and  it  therefore  throws  the  air  into 
similar  vibrations,  and  so  reproduces  the  sound.  Bell's 
method  of  transmitting  was  soon  abandoned  (except  for 
very  short  lines).  In  modern  telephonic  work  Reis's 
plan  of  using  a  separate  transmitter  with  a  battery  is 
universal,  the  Bell  instrument  being  used  us  a  receiver 
only  and  not  as  a  transmitter. 

511.  Edison's   Transmitter.  —  Edison   constructed  a 
transmitting  instrument,  in  which  the  vibrations  of  the 
voice,  actuating  a  diaphragm  of  mica,  made  it  exert  more 
or  less  compression  on  a  button  of  prepared  lamp-black 
placed  in  the  circuit.     The  resistance  of  this  is  affected 
by  pressure  of  contacts ;  hence  the  varying  pressures  due 
to   the  vibrations  cause   the   button  to  offer  a  varying 
resistance  to  any  current  flowing  (from  a  battery)  in  the 
circuit,  and  vary  its  strength  accordingly.     This  varying 
current  may  be  received  as  before  in  an  electromagnetic 
receiver  of  the  type  described  above,  and  there  set  up 
corresponding  vibrations.     This  instrument  also  has  been 
abandoned  in  favour  of  transmitters  of  the  microphone 
type.     Edison  also  invented  a  receiver  of  singular  power, 
which  depends  upon  a  curious  fact  discovered  by  himself, 
namely,  that  if  a  platinum  point  presses  against  a  rotating 
cylinder  of  moist  chalk,  the  friction  is  reduced  when  a 
current   passes  between  the  two.     And  if    the   point  be 
attached  to  an  elastic  disk,  the  latter   is  thrown   into 
vibrations    corresponding   to    the    fluctuating    currents 
coming  from  the  speaker's  transmitting  instrument. 

512.  Microphones.  —  Hughes,   in    1878,   discovered 
that  a  loose  contact  between  two  conductors,  forming  part 
of  a  circuit  in  which  a  small   battery  and  a  receiving 
telephone  are  included,  may  serve   to   transmit  sounds 
without  the  intervention  of   any  specific  tympanum  or 
diaphragm  like  those  of   Reis  and  Edison,  because  the 
smallest  vibrations  will  affect  the  resistance  (Art.  400)  at 
the  point  of  loose  contact.     The  Microphone  (Fig.  288) 


CHAP.    XIII 


MICROPHONES 


551 


embodies  this  principle.  In  the  form  shown  in  the 
figure,  a  small  thin  pencil  of  carbon  is  supported  loosely 
between  two  little  blocks  of  the  same  substance  fixed  to  a 
sounding-board  of  thin  pine-wood,  the  blocks  being  con- 
nected with  one  or  twro  small  cells  and  a  Bell  receiver. 
The  amplitude  of  the  vibrations  emitted  by  the  receiver 
may  be  much  greater  than  those  of  the  original  sounds, 


Vis. 


and  therefore  the  microphone  may  serve,  as  its  name 
indicates,  to  magnify  minute  sounds,  such  as  the  ticking 
of  a  watch  or  the  footfalls  of  an  insect,  and  render  them 
audible.  In  modern  telephony  microphones  under  the 
name  of  carbon  transmitters  are  in  general  use.  In  the 
Blake  transmitter  a  pin  of  platinum  is  pressed  by  a  light 
spring  against  a  polished  plug  of  hard  carbon,  forming  a 
delicate  contact  through  which  the  current  flows.  This 
electrical  mechanism  is  mounted  behind  a  metal  disk  to 
take  up  the  vibrations  of  the  speaker's  voice.  In  the 
Iluimings  loud-speaking  transmitter  granulated  coke 
carbon  is  placed  loosely  between  two  metal  surfaces,  so 


652 


ELECTRICITY  AND   MAGNETISM      PART  n 


that  the  current  flows  through  the  loose  particles.     The 
voice  acts  on  all  the  loose  contacts  at  once. 

513.  Telephone  Exchanges.  —  For  enabling   a  large 
number   of   subscribers   to  communicate    by  telephone 
with  one  another,  the  lines  from  each  subscriber's  instru- 
ment are  brought  to  a  central  office  known  as  a  telephone 
exchange.      Here  each  line  terminates  on  a  switch-board 
which  is  so  arranged  that  the  operator  can  in  an  instant 
make  a  connexion  from  the  line  of  any  one  subscriber  to 
that  of  any  other,  so  that  these  two  cr  i  talk  together. 

514.  Hughes's    Induction    Balance.  —  The    extreme 
sensitiveness  of  Bell's  receiver  (Art.  510)  to  the  feeblest 
currents  has  suggested  its  employment  to  detect  currents 
too  weak  to  affect  the  most  delicate  galvanometer.      The 
currents  must,  however,  be  intermittent,  or  they  will  not 
keep  the  disk  of  the  telephone  in  vibration.      Hughes 
applied  this  property  of  the  telephone  to  an  instrument 


Fig.  289. 

named  the  Induction  Balance  (Fig.  289) .  A  small  bat- 
tery B,  connected  with  a  microphone  M,  passes  through 
two  coils  of  wire  Pv  P2,  wound  on  bobbins  fixed  on  a 
suitable  stand.  Above  each  of  these  primary  coils  are 
placed  two  secondary  coils,  Sr  S2,  of  wire,  of  the  same 
size,  and  of  exactly  equal  numbers  of  turns  of  wire.  The 
secondary  coils  are  joined  to  a  receiver  T,  and  are  wound 
in  opposite  directions.  The  result  of  this  arrangement  is 


CHAP,  xni  INDUCTION  BALANCE  553 

that  whenever  a  current  either  begins  or  stops  flowing  in 
the  primary  coils,  P!  induces  a  current  in  Sr  and  P2  in 
S2.  As  Sj  and  S3  are  wound  in  opposite  ways,  the  two 
currents  thus  induced  in  the  secondary  wire  neutralize 
one  another,  and,  if  they  are  of  equal  strength,  balance 
one  another  so  exactly  that  no  sound  is  heard  in  the  tele- 
phone. But  a  perfect  balance  cannot  be  obtained  unless 
the  resistances  and  the  coefficients  of  mutual  induction 
and  of  self-induction  are  alike.  If  a  flat  piece  of  silver  or 
copper  (such  as  a  coin)  be  introduced  between  Sx  and  PI} 
there  will  be  less  induction  in  Sx  than  in  S2,  for  part  of 
the  inductive  action  in  Pl  is  now  spent  on  setting  up 
currents  in  the  mass  of  the  metal  (Art.  459),  and  a  sound 
will  again  be  heard  in  the  telephone.  But  balance  can 
be  restored  by  moving  S2  farther  away  from  P2,  until  the 
induction  in  S2  is  reduced  to  equality  with  Sv  when  the 
sounds  in  the  telephone  again  cease.  It  is  possible  by 
this  means  to  test  the  relative  conductivity  of  different 
metals  which  are  introduced  into  the  coils.  It  is  even 
possible  to  detect  a  counterfeit  coin  by  the  indication 
thus  afforded  of  its  conductivity.  The  induction  balance 
has  also  been  applied  in  surgery  by  Graham  Bell  to 
detect  the  presence  of  a  bullet  in  a  wound,  for  a  lump  of 
metal  may  disturb  the  induction  when  some  inches 
distant  from  the  coils. 


CHAPTER   XIV 

ELECTRIC    WAVES 

LESSON  LIV.  —  Oscillations  and  Waves 

515.  Electric  Oscillations.  —  If  a  charged  condenser 
or  Leyden  jar  is  discharged  slowly  through  a  conductor 
of  high  resistance,  such  as  a  nearly  dry  linen  thread, 
the  charge  simply  dies  away  by  a  discharge  which 
increases  in  strength  at  first,  and  then  gradually  dies 
away.  If,  however,  the  condenser  is  discharged  through 
a  coil  of  wire  of  one  or  more  turns  (the  spark  being  taken 
between  polished  knobs  to  prevent  premature  partial  dis- 
charge^ by  winds  or  brushes)  the  effect  is  wholly  different, 
for  then  the  discharge  consists  of  a  number  of  excessively 
rapid  oscillations  or  surgings.  This  is  in  consequence  of 
the  self-induction  of  the  circuit,  by  reason  of  which  (Art. 
458)  the  current  once  set  up  tends  to  go  on.  The  first 

rush  more  than  empties  the 
condenser,  and  charges  it  the 
opposite  way ;  then  follows  a 
i/v/vywvyv^  •—  reverse  discharge,  which  also 
overdoes  the  discharge,  and 
charges    the    condenser    the 
Pi     290  same  way  as  at  first,  and  so 

forth.    Each  successive  oscil- 
lation is  feebler  than  the  preceding,  so  that  after  a  number 
of  oscillations  the  discharge  dies  away  as  in  Fig.  290.    The 
554 


CHAP,  xiv        ELECTRIC   OSCILLATIONS  555 

spark  of  a  jar  so  discharged  really  consists  of  a  number 
of  successive  sparks  in  reverse  directions.  One  proof  of 
this,  as  pointed  out  by  Henry  in  1842  from  the  experi- 
ments of  Savery,  is  that  if  jar  discharges  through  a  coil 
are  used  to  magnetize  steel  needles,  the  direction  of  the 
magnetization  is  anomalous,  being  sometimes  one  way, 
sometimes  the  other. 

That  a  discharge  ought  under  certain  conditions  to 
become  oscillatory  was  noted  by  Von  Helmholtz.  Lord 
Kelvin  in  1855  predicted  these  conditions.  If  the  capacity 
of  the  condenser  is  K  (farads ),  the  resistance  of  the  cir- 
cuit R  (ohms),  and  its  inductance  L  (henries),  there  will 

be  oscillations  if  

R<V4L7K"; 

and  there  will  be  no  oscillations  if 


In  the  former  case  the  frequency  n  of  the  oscillations  will 
be  such  that  

2*n=JTI^. 
>KL     4L2 

Example.  —  If  K  =  0'01  microfarad,  L  =  0-00001  henry,  and 
R  =  0,  n  =  503,000. 

If  R  is  small  n  is  nearly  equal  to  1  -4-  2«-VKL. 

The  oscillations  can  be  made  slower  by  increasing  either 
K  or  L.  The  oscillations  of  an  ordinary  Leyden  jar  dis- 
charge may  last  only  from  a  ten-thousandth  to  a  ten- 
millionth  of  a  second.  By  using  coils  of  well-insulated 
wire  and  large  condensers,  Lodge  has  succeeded  in  slowing 
down  the  oscillations  to  400  a  second;  the  spark  then 
emitting  a  musical  note.  Iron  is  found  to  retain  its 
magnetic  properties  even  for  oscillations  of  the  frequency 
of  one  million  per  second. 

Feddersen    subsequently  examined   the   spark    of    a 
Leyden  jar  by  means  of  a  rotating  mirror,  and  found  that 


556  ELECTRICITY   AND   MAGNETISM       PART  n 


instead  of  being  a  single  instantaneous  discharge,  it 
exhibited  definite  fluctuations.*  With  very  small  resist- 
ances in  the  circuit,  there  was  a  true  oscillation  of  the 
electricity  backward  and  forward  for  a  brief  time.  The 
period  of  the  oscillations  was  found  to  be  proportional  to 
the  square  root  of  the  capacity  of  the  condenser.  With 
a  certain  higher  resistance  the  discharge  became  continu- 
ous but  not  instantaneous.  With  a  still  higher  resistance 
the  discharge  consisted  of  a  series  of  partial  intermittent 
discharges,  following  one  another  in  the  same  direction. 
Such  sparks  when  viewed  in  the  rotating  mirror  showed 
a  series  of  separate  images  at  nearly  equal  distances  apart. 

516.  Electric  Waves.  —  Though  the  increasing  and 
dying  away  of  currents,  for  example  in  cables,  is  some- 
times loosely  described  as  of  "  waves  "  of  current,  these 
phenomena  are  very  different  from  those  of  true  electric 
or  electromagnetic  ivaves  propagated  across  space.  In  the 
case  of  true  electric  waves,  portions  of  the  energy  of  the 
current  or  discharge  are  thrown  off  from  the  conductor 
and  do  not  return  back  to  it,  but  go  travelling  on  in 
space.  If  a  current  increases  in  strength  the  magnetic 
field  around  it  also  increases,  the  magnetic  lines  enlarging 
from  the  conductor  outward,  like  the  ripples  on  a  pond. 
But  as  the  current  is  decreased  the  magnetic  lines  all 
return  back  and  close  up  upon  the  conductor ;  the  energy 
of  the  magnetic  field  returns  back  into  the  system.  But 
if  for  currents  slowly  waxing  and  waning  we  substitute 
electric  oscillations  of  excessive  rapidity,  part  of  their 
energy  radiates  off  into  the  surrounding  medium  as 
electromagnetic  waves,  and  only  part  returns  back.  As 
will  be  presently  set  forth,  these  waves  possess  all  the 
optical  properties  of  light-waves,  and  can  be  reflected, 
refracted,  polarized,  etc. 

It  is  a  fundamental  part  of  the  modern  views  of  electric 
action  that  while  an  electric  displacement  (Art.  57)  is 

*  These  electric  oscillations  were  examined  also  "by  Schiller,  Over- 
beck,  Blaserna,  and  others,  notably  by  Hertz ;  see  Art.  520  below. 


CHAP,  xiv  RESONANCE  557 

being  produced  in  a  dielectric,  the  effect  in  surrounding 
space  is  the  same  as  if  there  had  been  a  conductive  instead 
of  an  inductive  transfer  of  electricity.  Maxwell  gave  the 
name  of  displacement-current  to  the  rate  of  change  of 
the  displacement.  Experiment  proves  that  displace- 
ment-currents, while  they  last,  set  up  magnetic  fields 
around  them ;  just  as  convexion-curreiits  (Art.  397)  and 
conduction-currents  do. 

517.  Resonance.  —  The  circumstance  that  when 
certain  definite  relations  exist  between  the  capacity  and 
inductance  of  a  circuit  and  the  frequency  of  the  periodic 
currents,  the  choking  reactions  of  these  properties  neu- 
tralize one  another,  has  been  already  alluded  to  in  Art. 
473.  And  we  have  seen  (Art.  515)  that  a  circuit  with  a 
certain  self-induction,  capacity,  and  resistance  tends  to 
oscillate  electrically  at  a  certain  frequency.  If  it  be 
placed  in  a  medium  through  which  electric  waves  of  that 
frequency  are  passing  in  such  a  position  that  the  electric 
and  electromagnetic  fields  of  the  successive  waves  can 
induce  currents  in  it,  each  wave  will  give  a  slight  im- 
pulse to  the  readily-excited  oscillations,  which  will  grow 
in  intensity,  just  as  small  impulses  given  to  a  pendulum 
at  the  right  times  will  make  it  swing  violently. 

The  following  experiment  of  Oliver  Lodge  beautifully 
illustrates  this  phenomena  of  resonance,  and  at  the  same 
time  the  production  of  waves 
by  an  oscillatory  discharge. 
Two  Leyden  jars,  Fig.  291, 
are  placed  a  little  way  apart 
from  one  another.  One  of 
them,  charged  from  an  in- 
fluence machine  not  shown, 
is  provided  with  a  bent  wire 
to  serve  as  a  discharging 

•pjp.     OO1 

circuit,  with  a  spark-gap  S 

between  the  polished  knobs  at  the  top.     The  second  jar  is 

provided  with  a  circuit  of  wire,  the  inductance  of  which 


558  ELECTRICITY   AND   MAGNETISM      PART  n 

can  be  adjusted  by  sliding  in  or  out  a  cross-piece  W 
hooked  upon  the  other  portions.  A  strip  of  tinfoil  is 
brought  up  from  the  inner  coating  over  the  lip  of  this 
jar,  but  does  not  quite  touch  the  outer  coating.  If  the 
two  circuits  are  properly  tuned  together,  whenever  a 
spark  passes  in  the  gap  at  the  top  of  A,  surgings  will 
be  set  up  in  the  circuit  of  B  which  will  cause  the  jar  to 
overflow,  producing  a  spark  at  the  end  of  the  strip. 


LESSON  LV.  —  The  Electromagnetic  Theory  of  Liy/tt 

518.  Maxwell's  Theory.  — In  1867  Clerk  Maxwell 
put  forward  the  theory  that  the  waves  of  light  are  not 
mere  mechanical  motions  of  the  ether,  but  that  they  are 
electrical  undulations.  These  undulations  are  partly 
electrical  and  partly  magnetic,  oscillating  electrical  dis- 
placements being  accompanied  by  oscillating  magnetic 
fields  at  right  angles  to  them,  whilst  the  direction  of 
propagation  of  the  wave  is  at  right  angles  to  both. 
According  to  this  theory  the  phenomena  of  electro- 
magnetism  and  the  phenomena  of  light  are  all  due  to 
certain  modes  of  motion  in  the  ether,  electric  currents 
and  magnets  being  due  to  streams  and  whirls  or  other 
bodily  movements  in  the  substance  of  the  ether,  while 
light  is  due  to  vibrations  to  and  fro  in  it. 

An  electric  displacement  in  its  growth  or  decay  pro- 
duces a  magnetic  force  at  right  angles  to  itself;  it  also 
produces  (by  the  peculiar  action  known  as  induction, 
an  electric  force  which  is  propagated  at  right  angles 
both  to  the  electric  displacement  and  to  the  magnetic 
force.  Now  it  is  known  that  in  the  propagation  of 
light  the  actual  displacements  or  vibrations  which  con- 
stitute the  so-called  ray  of  light  are  executed  in  directions 
at  right  angles  to  the  direction  of  propagation.  This 
analogy  is  an  important  point  in  the  theory,  and  imme- 
diately suggests  the  question  whether  the  respective  rates 


CHAP.    XIV 


MAXWELL'S   THEORY 


559 


of  propagation  are  the  same.  Now  the  velocity  of  propa- 
gation of  electromagnetic  induction  is  that  velocity  "  v  " 
which  was  shown  (Art.  359)  to  represent  the  ratio  between 
the  electrostatic  and  the  electromagnetic  units,  and  which 
(in  air)  has  been  found  to  be 

2-9857  x  1010  centimetres  per  second. 

And  the  velocity  of  light  (in  air)  has  been  repeatedly 
measured  (by  Fizeau,  Cornu,  Michelson,  and  others), 
giving  as  the  approximate  value 

2-9992  x  1010  centimetres  per  second. 

From  the  equations  for  the  propagation  of  a  disturb- 
ance in  an  electromagnetic  medium,  having  dielectric 
coefficient  k  (Art.  295)  and  permeability  fj.  (Art.  363),  it 
was  calculated  by  Maxwell  that  the  velocity  ought  to  be 
numerically  —  I/  Vfyt.  And,  as  we  have  seen,  this  quan- 
tity enters  into  the  ratio  of  the  units  (Art.  360),  and 
can  be  calculated  from  them.  It  follows  that  if  there 
are  two  transparent  media  of  equal  permeability,  but 
different  dielectric  capacities,  the  velocities  in  them  ought 
to  vary  relatively  inversely  as  VI-.  But  the  ratio  of  the 
velocities  of  light  in  them  is  called  their  refractive  index. 
Hence  if  Maxwell's  theory  is  true,  the  dielectric  capacity 
of  ordinary  transparent  media  ought  to  be  equal  to  the 
square  of  the  refractive  index.  Experiments  by  Gordon, 


k. 

(Index)  2. 

Flint  Glass 

3-162 

2-796 

Bisulphide  of  Carbon 

1-812 

2-606 

Sulphur  (mean) 

4-151 

4-024 

Paraffin 

2-32 

2-33 

Boltzmann,  and  others,  show  this  to  be  approximately 
true  for  waves  of  very  great  wave-length.     The  values 


560  ELECTRICITY   AND   MAGNETISM      PART  11 

are   shown  below.     For  gases  the  agreement  is  even 
closer. 

Another  consequence  of  the  theory  is  that  all  con- 
ductors, since  they  dissipate  the  energy  of  the  currents  set 
up  in  them,  ought  to  be  opaque  to  light.  Metallic  con- 
ductors are,  except  when  in  very  thin  films.  But  electro- 
lytic liquids  are  not  opaque,  the  mechanism  of  their  con- 
duction being  different  (Art.  490).  In  some  crystalline 
bodies  which  conduct  electricity  better  in  one  direction 
than  in  another,  the  opacity  to  light  differs  correspond- 
ingly. Coloured  crystals  of  Tourmaline  conduct  electricity 
better  across  the  long  axis  of  the  crystal  than  along  that 
axis.  Such  crystals  are  much  more  opaque  to  light  pass- 
ing along  the  axis  than  to  light  passing  across  it.  And, 
in  the  case  of  rays  traversing  the  crystal  across  the  axis, 
the  vibrations  across  the  axis  are  more  completely  ab- 
sorbed than  those  parallel  to  the  axis :  whence  it  follows 
that  the  transmitted  light  will  be  polarized. 

519.  Energy  Paths.  —  From  Maxwell's  equations 
Poynting  in  1883  drew  the  conclusion  that  in  all  cases 
where  energy  is  transferred  in  an  electric  system  it  flows 
parallel  to  the  surfaces  of  both  electric  and  magnetic 
equipotentials.  What  we  call  an  electric  current  along 
a  wire  is  rather  a  transfer  of  energy  by  an  invisible 
mechanism  in  the  medium  outside  the  wire.  Wherever 
in  the  wire  there  is  resistance,  wasting  energy  by  degrad- 
ing it  into  heat,  at  that  point  energy  flows  in  laterally  from 
the  medium.  According  to  this  view,  the  service  of  the 
wire  is  merely  to  guide  the  energy  flow  going  on  outside 
it.*  We  know  that  when  a  current  is  started  much 
energy  is  spent  in  building  up  around  the  conductor  a 
magnetic  field,  the  amount  spent  being  £LC2  (Art.  458). 
When  the  circuit  is  "broken"  this  energy  flows  on  lat- 
erally into  the  wire,  giving  rise  to  the  so-called  extra- 
current  sparks.  According  to  Poynting's  view,  which 
has  been  independently  elaborated  by  Heaviside,  all  the 

*  See  particularly  Oliver  Lodge's  Modern  Views  of  Electricity. 


CHAP,  xiv         RESEARCHES   OF   HERTZ  561 

energy  flows  in  similarly.  In  the  case  of  the  transfer  of 
energy  in  an  alternate  current  transformer  from  the  coils 
of  the  primary  circuit  to  those  of  the  secondary,  it  is  pretty 
obvious  that  the  flow  of  energy  must  take  place  laterally 
to  the  copper  wires ;  and  it  also  takes  place  laterally  to 
the  iron  wires  of  the  core,  though  this  is  not  so  obvious. 

52O.  Researches  of  Hertz.  — In  1888  Hertz  found 
the  most  convincing  experimental  proofs  of  Maxwell's 
theory,  and  succeeded  in  producing  electromagnetic  waves 
in  a  way  which  permitted  him  to  examine  their  propaga- 
tion through  space,  and  to  show  that,  while  they  were 
much  larger  than  ordinary  waves  of  light,  they  possessed 
the  same  properties,  travelled  at  the  same  speed,  and  were 
capable  of  being  reflected,  refracted,  polarized,  etc. 

Of  the  power  of  oscillatory  discharges  to  propagate 
disturbances  in  the  surrounding  space  something  was 


OSCILLATOR.  RESONATOR. 

Fig.  292.  Fig.  293. 

already  known.  Henry  had  shown  that  they  set  up 
other  sparks  in  distant  conducting  circuits.  It  had  been 
discovered*  that  a  spark-gap  in  the  exciting  circuit  was 
necessary.  Fitzgerald  had  definitely  proposed  to  start 
waves  by  the  oscillatory  discharges  of  small  condensers. 
But  no  one  had  systematically  followed  out  the  phe- 
nomena of  propagation  of  the  waves. 

Hertz  employed  to  start  the  waves  an  apparatus  called 
an  oscillator  (Fig.  292),  consisting  of  two  metallic  con- 
ductors (balls  or  plates)  united  by  a  metal  rod,  at  the 

*  See  paper  by  the  author  in  the  Philosophical  Magazine  (Septem- 
ber, 18T6). 

2  o 


562 


ELECTRICITY   AND    MAGNETISM      PART  n 


middle  of  which  was  interposed  a  spark-gap  between  two 
well-polished  knobs.  And  to  detect  the  waves  at  a 
distance  he  employed  a  resonator,  simply  a  circle  or  square 
of  wire,  having  in  it  a  spark-gap  capable  of  minute 
adjustment.  In  one  experiment  the  oscillator  consisted 
of  two  zinc  plates  A  and  B  (Fig.  292)  with  sides  40  cm. 
long  mounted  60  cm.  apart,  and  having  stout  copper 
wires  leading  to  a  spark-gap  between  very  brightly 
polished  brass  balls.  A  dry  wood  stand  was  a  sufficient 
insulator.  The  resonator  to  match  was  a  circle  35  cm. 
in  radius.  To  experiment  with  this  apparatus  the 
oscillator  is  joined  to  a  small  induction  coil.  When 


Fig.  294. 

a  spark  snaps  across  the  gap  it  sets  up  a  temporary  con- 
ducting path  for  the  surgings  that  follow.  For  a  rush  of 
current  from  left  to  right  overcharges  the  right-hand  plate, 
and  so  there  follows  a  rush  back  from  right  to  left,  and  so 
on .  Each  spark  sent  by  the  coil  across  the  gap  consists  of  a 
dozen  or  so  oscillations  each  lasting  less  than  1/100,000,000 
of  a  second,  the  period  being  determined  (Art.  515)  by  the 
capacity  and  inductance  of  the  apparatus;  the  discharges 
surging  backward  and  forward  from  A  to  B  until  they 
die  out  (Fig.  290).  Let  the  line  drawn  horizontally  in 
Fig.  294  be  termed  the  base  line,  and  let  the  line  AB  be 
termed  the  line  of  oscillation.  Then  if  the  resonator  is 
placed  with  its  centre  on  the  base  line  at  a  few  feet  away 
from  the  oscillator  and  is  turned  into  various  positions, 


CHAP,  xiv         RESEARCHES   OF   HERTZ  563 

various  effects  are  observed.  If  the  resonator  is  set 
edge-on  vertically,  no  sparks  are  observed  in  it  whatever 
the  situation  of  the  gap  in  the  circle.  If  it  is  laid  edge- 
on  horizontally  sparks  pass  between  the  balls  of  the 
resonator.  These  are  brightest  when  the  gap-space  is 
nearest  toward  the  oscillator,  so  that  the  induced  spark 
is  parallel  to  the  primary  spark.  If  the  resonator  be 
now  turned  broadside  on  to  the  oscillator  it  will  be  found 
that  there  are  sparks  when  the  gap  is  at  the  top  or 
bottom  of  the  circle  —  so  that  the  sparks  are  parallel  to 
the  primary  spark ;  but  there  are  none  if  the  gap  is  at 
the  side.  The  primary  spark  does  not  here  induce  sparks 
at  right  angles  to  itself. 

The  reflexion  of  electric  waves  was  observed  in  various 
ways.  If  right  opposite  the  oscillator,  Fig.  292,  is  set  a 
large  metal  sheet  as  a  reflector,  to  send  back  the  waves 
that  pass  along  the  base  line,  stationary  nodes  will  be 
produced  at  regular  intervals.  If  the  resonator  is  put 
broadside  on,  with  its  gap  at  the  highest  point,  and 
moved  along  the  base  line  till  it  lies  flat  against  the 
reflector,  there  will  in  this  position  be  no  sparks ;  but  if 
it  is  slowly  moved  back  from  the  sheet  sparks  will  showr, 
will  come  to  a  maximum,  then  die  out  as  the  first  node 
is  reached  at  about  180  cm.  from  the  reflector.  Passing 
this  node  the  sparks  will  begin  again,  nodes  occurring  at 
equal  intervals  apart  along  the  base  line.  By  using 
large  parabolic  mirrors  Hertz  showed  that  these  electric 
waves  can  be  reflected  and  brought  to  a  focus  exactly  as 
light  waves  can  be.  Hertz  also  showed  refraction  with  a 
prism  of  pitch ;  and  polarization  by  means  of  gratings  of 
parallel  wires. 

Later  Tesla  showed  that  the  Hertzian  effects  could  be 
much  augmented  by  increasing  the  suddenness  of  the 
spark  by  using  a  magnetic  field  to  blow  it  out.  Elihu 
Thomson  uses  an  air-blast  across  the  spark-gap  for  the 
same  purpose. 

521.   Detectors  of  Electric  Waves.  —  The  Hertz  spark- 


564  ELECTRICITY  AND   MAGNETISM        PART  11 

gap  resonator  is  only  one  means  of  detecting  electric 
waves.  A  prepared  frog's  leg  (Art.  255)  may  be  used 
instead  of  a  spark-gap.  A  sensitive  vacuum  tube,  espe- 
cially if  primed  by  application  with  a  battery  of  some 
hundreds  of  small  cells  not  quite  able  of  themselves  to 
start  a  spark,  forms  a  good  explorer.  Electrometers ; 
thin  wires  capable  of  expanding  when  heated  by  the 
induced  currents  ;  and  galvanometers  in  circuit  with  the 
gap,  are  amongst  the  possible  means.  Best  of  all  is  Lodge's 
device  of  a  tube  partly  filled  with  coarse  iron  filings,  in- 
serted in  circuit  with  a  galvanometer  and  a  single  cell. 
The  resistance  of  the  filings  is  very  great,  and  little 
current  flows,  until  an  electric  wave  impinges  upon  the 
tube,  when  at  once  the  filings  conduct  (compare  Art.  400 
on  conductance  of  powders).  On  lightly  tapping  the 
tube  the  filings  fall  back  into  their  former  state.  Using 
such  a  detector,  and  an  oscillator  consisting  of  a  highly 
polished  brass  ball  between  two  smaller  balls,  Lodge  has 
shown  how  these  electric  waves  can  pass  hundreds  of  feet 
through  walls  and  floors  of  houses.  Care  must  be  taken  to 
screen  oft'  with  metallic  screens  the  effects  of  stray  sparks. 
522.  Properties  of  Electric  Waves.  —  The  universal 
equation  connecting  frequency  n,  wave-length  A,  and 
velocity  of  propagation  v  is :  v  =  nX.  Taking  v  (in 
air)  as  3  x  1010  (cms.  per  sec.)  as  the  velocity  of  light, 
and  the  measured  length  of  the  red  waves  (the  longest 
visible)  as  0-000076,  it  follows  that  the  frequency  of 
oscillation  of  these  must  be  no  less  than  395  x  1012. 
The  waves  artificially  produced  by  electric  oscillations 
are  of  much  lower  frequency  than  these,  and  their  wave- 
length proportionally  longer.  Their  wave-length  depends 
on  the  size  of  the  apparatus  used  as  oscillator,  just  as 
the  note  emitted  by  an  iron  cylinder  when  struck  on 
its  end  depends  on  the  length  of  the  cylinder.  The  wave- 
length of  waves  emitted  from  an  oscillator  consisting 
of  a  wire  with  a  small  capacity  at  each  end  is  twice 
the  length  of  the  wire.  That  of  waves  emitted  from 


CHAP,  xiv    PROPERTIES  OF  ELECTRIC  WAVES     565 


Fig.  295. 


a  sphere  (Fig.  295)  of  diameter  d  is  2ird/^/3  or  3-6  d: 
but  they  die  out  after  about  1  vibration.     If  a  spark-gap 
is  made  between  two  knobs  across  the   diameter   of   a 
hollow     cylinder,    the     wave- 
length of   the  waves  emitted 
from  the  end  of  the  cylinder 
is  about  equal  to  its  diameter, 
and  the  vibrations  are  numer- 
ous before  all  the  energy  has 
been   radiated    away.      Using 

symmetrical  pairs  of  con  den-    L_^ •••"_  1 

sers  carefully  adjusted  Ebert      fl 
has  obtained  oscillations  that  ^ 
do  not  die  out  till  after  20,000 
periods. 

The  currents  produced  in 

wires  by  oscillations  of  such  enormous  frequency  are  only 
skin-currents  (Art.  476),  the  inner  part  of  the  wire  being 
idle.  Hence  for  such  currents  the  impeding  resistance 
of  a  stout  copper  wire  may  be 
millions  of  ohms.  One  evidence 
of  this  is  afforded  by  the  tendency 
to  lateral  discharge.  This  is 
readily  shown  by  connecting- 
bet  ween  the  Ley  den  jars  of  an 
influence  machine  a  loop  of  stout 
copper  wire  bent  as  in  Fig.  296. 
When  a  discharge  takes  place 
between  the  knobs,  there  will  be 
an  oscillatory  current  set  up 

between  the  outer  coatings  also ;  and  this  oscillatory 
current  rather  than  flow  along  the  metal  loop  will  jump 
as  a  spark  across  the  parts  that  lie  nearest  together.  The 
tendency  of  lightning  to  produce  lateral  discharges  is 
relied  upon  by  Oliver  Lodge  in  his  contention  as  to  the 
oscillatory  character  of  the  flash. 

523.   Travelling   of   Waves    along    Wires.  —  If    an 


Fig.  296. 


566  ELECTRICITY    AND   MAGNETISM      PART  n 


oscillatory  spark  is  sent  into  one  end  of  a  long  wire,  by 
the  time  that  the  second  pulsation  reaches  its  maximum 
the  first  will  have  travelled  a  certain  distance  which  may 
be  called  the  wave-length  of  the  disturbance.  According 
to  Maxwell's  theory  the  velocity  of  propagation  will  be 
equal  to  that  of  light,  the  energy  really  travelling  through 
the  air,  and  settling  down  laterally  into  the 
wire.  It  appears  from  experiment  that  the 
velocity  of  a  wave  guided  by  a  wire  is 
C  the  same  as  that  of  a  wave  travelling  in 
free  air.  That  the  speed  of  travelling  is 
independent  of  the  thickness  or  materials  of 
the  wire  was  proved  in  1870  by  Von  Bezold 
using  the  device  of  Fig.  297.  Let  an 
oscillatory  discharge  be  sent  by  a  wire  at  G 
into  a  rectangular  circuit  ABCD,  having  a 
spark-gap  PQ  midway  between  B  and  D. 
It  is  evident  that  if  G  is  midway  between 


B     PQ 


A  and  C  the  impulses  will  arrive  simultaneously  at  P 
and  Q  if  both  sides  of  the  system  are  alike  ;  and  there 
will  be  no  spark.  If  now  one  side,  say  CD,  be  made  of 
iron  and  the  other,  AB,  of  copper,  it  will  be  found  that 
still  the  discharge  must  be  led  in  at  G,  exactly  midway 
if  there  is  to  be  no  spark. 


LESSON  LVI.  —  Other  Relations  between  Light  and 
Electricity 

524.  Electro-optical  Phenomena.  —  Of  late  years 
several  important  relations  have  been  observed  between 
electricity  and  light.  These  observations  may  be  classi- 
fied under  the  following  heads  :  — 

(i.)  Production   of  double  refraction   by   dielectric 

stress. 
(ii.)  Rotation  of  plane  of  polarization  of  a  wave  of 


CHAP,  xiv    ELECTROSTATIC   OPTICAL  STRESS     567 

light  on  traversing  a  transparent  medium  placed 

in  a  magnetic  field,  or  by  reflexion  at  the  surface 

of  a  magnet, 
(iii.)  Change    of     electric     resistance,     exhibited    by 

selenium  and  other   bodies   during   exposure  to 

light. 

(iv.)  Photo-chemical  excitation  of  electromotive  forces. 
(v.)  Relation  between  refractive  index  and  dielectric 

capacity  of  transparent  bodies, 
(vi.)  Electric  effect  of  ultra-violet  light. 

It  was  announced  by  Mrs.  Somerville,  by  Zantedeschi,  and 
others,  that  steel  needles  could  be  magnetized  by  exposing 
portions  of  them  to  the  action  of  violet  and  ultra-violet  rays  of 
light;  the  observations  were,  however,  erroneous. 

Bidwell  has  found  that  light  falling  upon  a  recently  de- 
magnetized piece  of  iron  produces  an  instantaneous  revival  of 
magnetism. 

525.  Electrostatic  Optical  Stress.  —  In  1875  Dr.  Kerr 
of  Glasgow  discovered  that  glass  when  subjected  to  a 
severe  electrostatic  stress  undergoes  an  actual  strain, 
which  can  be  observed  by  the  aid  of  a  beam  of  polarized 
light.  In  the  original  experiment  two  wires  were  fixed 
into  holes  drilled  in  a  slab  of  glass,  but  not  quite  meeting, 
so  that  when  these  were  placed  in  connexion  with  the 
terminals  of  an  induction  coil  or  of  an  influence  machine 
the  accumulating  charges  on  the  wires  subjected  the 
intervening  dielectric  to  an  electrostatic  tension  along 
the  electric  lines  of  force.  The  slab  when  placed  between 
two  Mcol  prisms  as  polarizer  and  analyzer*  exhibited 
double  refraction,  as  if  it  had  been  subjected  to  a  pull 
and  had  expanded  along  the  direction  of  the  electric 
force.  Bisulphide  of  carbon  and  other  insulating  liquids 
exhibit  similar  phenomena,  but  fatty  oils  of  animal  and 

*  A  ray  of  light  is  said  to  be  polarized  if  the  vibrations  take  place  in 
one  plane.  Ordinary  light  can  be  reduced  to  this  condition  by  passing  it 
through  a  suitable  polarizing  apparatus  (such  as  a  Nicol  prism,  a  thin  slice 
of  tourmaline  crystal,  etc.). 


568  ELECTRICITY  AND   MAGNETISM      PART  il 

vegetable  origin  exhibit  an  action  in  the  negative  direc- 
tion, as  if  they  had  contracted  along  the  electric  lines. 
It  is  found  that  the  difference  of  retardation  between 
the  ordinary  and  extraordinary  waves  per  unit  thickness 
of  the  dielectric  is  proportional  to  the  square  of  the  result- 
ant electric  force.  The  axis  of  double  refraction  is 
along  the  line  of  the  electric  force.  Quincke  has  pointed 
out  that  these  phenomena  can  be  explained  by  the  exist- 
ence of  electrostatic  expansions  and  contractions  stated 
in  Art.  300. 

526.  Magneto-optic  Rotation  of  the  Plane  of  Polari- 
zation of  Light.  —  In  1845  Faraday  discovered  that  a 
wave  of  light  polarized  in  a  certain  plane  can  be  twisted 
round  by  the  action  of  a  magnet,  so  that  the  vibrations 
are  executed  in  a  different  plane.  The  plane  in  which  a 
beam  is  polarized  can  be  detected  by  observing  it  through 
a  second  Mcol  prism  (or  tourmaline),  for  each  such 
polarizer  is  opaque  to  waves  polarized  in  a  plane  at  right 
angles  to  that  plane  in  which  it  would  itself  polarize 
light.  Faraday  caused  a  polarized  beam  to  pass  through 
a  piece  of  a  certain  "  heavy  glass  "  (consisting  chiefly  of 
borate  of  lead),  lying  in  a  powerful  magnetic  field,  be- 
tween the  poles  of  a  large  electromagnet,  through  the 
coils  of  which  a  current  could  be  sent.  In  the  path  of 
the  emerging  beam  was  placed  as  analyzer  a  second  Mcol 
prism  which  had  been  turned  round  until  all  the  light 
was  extinguished.  In  this  position  its  own  plane  of  sym- 
metry was  at  right  angles  to  the  plane  of  polarization  of 
the  beam.  On  completing  the  circuit,  light  was  at  once 
seen  through  the  analyzing  Nicol  prism,  proving  that  the 
waves  had  been  twisted  round  into  a  new  position,  in 
which  the  plane  of  polarization  was  no  longer  at  right 
angles  to  the  plane  of  symmetry  of  the  analyzer.  But  if 
the  analyzing  Nicol  prism  was  itself  turned  round,  a  new 
position  could  be  found  (at  right  angles  to  the  plane  of 
polarization  of  the  waves)  at  which  the  light  was  once 
more  extinguished.  The  direction  of  the  magneto-optic  rota- 


CHAP,  xiv       ROTATION  OF  LIGHT-  WAVES  569 

tion  of  the  plane  of  polarization  is  the  same  (for  diamagnetic 
media)  as  that  in  which  the  current  flows  which  produces  the 
magnetism.  Verdet  discovered  the  important  law  that, 
with  a  given  material,  the  amount  'of  rotation  is  propor- 
tional to  the  strength  of  the  magnetic  force  H.  In  case  the 
waves  do  not  pass  straight  along  the  direction  of  the 
field,  the  amount  of  rotation  is  proportional  to  the  cosine 
of  the  angle  ft  between  the  direction  of  the  beam  and  the  lines 
of  force.  It  is  also  proportional  to  the  length  I  of  the 
material  through  which  the  waves  pass.  These  laws  are 
combined  in  the  equation  for  the  rotation  6  : 


where  w  is  a  coefficient  which  represents  the  specific 
magnetic  rotatory  power  of  the  given  substance,  and  is 
known  as  Verde?  s  constant.  Now,  H  •  cos/?  •  I  is  the 
difference  of  magnetic  potential  between  the  point  A 
where  the  wave  enters  and  B  where  it  leaves  the  medium. 
Hence 


The  value  of  Verdet's  constant  for  yellow  sodium 
light,  at  18°  C.,  has  been  carefully  determined.  Its  value 
(in  radians  per  unit  fall  of  magnetic  potential)  is,  in 
bisulphide  of  carbon  1-222  x  10~5;  in  water  0-375  x  10~5; 
in  heavy  glass  2-  132  x  10~5.  For  diamagnetic  substances 
the  coefficient  is  usually  positive  ;  but  in  the  case  of 
many  magnetic  substances,  such  as  solutions  of  ferric 
chloride,  has  a  negative  value  (i.e.  in  these  substances  the 
rotation  is  in  the  opposite  direction  to  that  in  which  the 
magnetizing  current  flows).  The  phenomenon  discovered 
by  Hall  (Art.  397)  appears  to-be  intimately  related  to 
the  phenomenon  of  magneto-optic  rotation.  For  light 
of  different  colours  the  rotation  is  not  equal,  but  varies 
very  nearly  inversely  as  the  square  of  the  wave-length. 

Gases  also  rotate  the  plane  of  polarization  of  light  in 


570  ELECTRICITY  AND   MAGNETISM      PART  n 

a  magnetic  field  with  varying  amounts;  coal-gas  and 
carbonic  acid  being  more  powerful  than  air  or  hydrogen  ; 
oxygen  and  ozone  being  negative.  The  rotation  is  in  all 
cases  very  slight,  and  varies  for  any  gas  in  proportion  to 
the  quantity  of  gas  traversed.  H.  Becquerel  has  shown 
that  the  plane  of  the  natural  polarization  of  the  sky  does 
not  coincide  with  the  plane  of  the  sun,  but  is  rotated  by 
the  influence  of  the  earth's  magnetism  through  an  angle 
which,  however,  only  reached  59'  of  arc  at  a  maximum 
on  the  magnetic  meridian. 

We  have  seen  (Arts.  126,  397,  and  398)  what  evidence  there 
is  for  thinking  that  magnetism  is  a  phenomenon  of  rotation,  there 
being  a  rotation  of  something  around  an  axis  lying  in  the  direction 
of  the  magnetization.  Such  a  theory  would  explain  the  rotation 
of  the  plane  of  polarization  of  a  ray  passing  through  a  magnetic 
field.  For  a  ray  of  plane-polarized  light  may  be  conceived  of  as 
consisting  of  a  pair  of  (oppositely)  circularly-polarized  waves,  in 
which  the  right-handed  rotation  in  one  ray  is  periodically  counter- 
acted by  an  equal  left-handed  rotation  in  the  other  ray ;  and  if 
such  a  motion  were  imparted  to  a  medium  in  which  there  were 
superposed  a  rotation  (such  as  we  conceive  to  take  place  in  every 
magnetic  field)  about  the  same  direction,  one  of  these  circularly- 
polarized  rays  would  be  accelerated  and  the  other  retarded,  so 
that,  when  they  were  again  compounded  into  a  single  plane- 
polarized  ray,  this  plane  would  not  coincide  with  the  original 
plane  of  polarization,  but  would  be  apparently  turned  round 
through  an  angle  proportional  to  the  superposed  rotation. 

527.  Kerr's  Effect  — Dr.  Kerr  showed  in  1877  that 
a  ray  of  polarized  light  is  also  rotated  when  reflected 
at  the  surface  of  a  magnet  or  electromagnet.  When  the 
light  is  reflected  at  a  pole  the  plane  of  polarization  is 
turned  in  a  direction  contrary  to  that  in  which  the 
magnetizing  current  flows.  If  the  light  is  reflected  at  a 
point  on  the  side  of  the  magnet  it  is  found  that  when 
the  plane  of  polarization  is  parallel  to  the  plane  of 
incidence  the  rotation  is  in  the  same  direction  as  that 
of  the  magnetizing  current ;  but  that,  when  the  plane  of 
polarization  is  perpendicular  to  the  plane  of  incidence, 
the  rotation  is  in  the  same  direction  as  that  of  the 


CHAP,  xiv      PROPERTIES   OF   SELENIUM  571 

magnetizing  current  only  when  the  incidence  exceeds 
75°,  being  in  the  opposite  direction  at  lesser  angles  of 
incidence. 

528.  Kundt's  Effect.  —  Kundt  found  that  the  plane 
of  polarization  of  light-waves  is  also  rotated  if  the  light 
is  passed  through  a  film  of  iron  so  thin  as  to  be  trans- 
parent, if  placed  transversely  in  a  magnetic  field. 

529.  Photo-electric    Properties    of    Selenium.  —  In 
1873  Willoughby   Smith   announced   the   discovery   (by 
J.  E.  Mayhew),  that  the  element  selenium  possesses  the 
abnormal  property  of   changing    its    electric   resistance 
under  the  influence  of  light.     Ordinary  fused  or  vitreous 
selenium  is  a  very  bad  conductor ;   its  resistance  being 
nearly  forty-thousand-million  (3  •  8  x  1010)  times  as  great 
as  that  of  copper.     When  carefully  annealed  (by  keeping 
for  some  hours  at  a  temperature  of  about  220°  C.,  just 
below  its  fusing  point,  and  subsequent  slow  cooling)  it 
assumes   a  crystalline   condition,   in   which    its  electric 
resistance  is  considerably  reduced.     In  the  latter  condi- 
tion, especially,  it  is  sensitive  to  light.     Adams  found 
that  greenish-yellow  rays  were  the   most  effective.     He 
also  showed  that  the  change  of  electric  resistance   varies 
directly  as  the  square  root  of  the  illumination,  and  that  the 
resistance  is  less  with  a  high  electromotive-force  than  a 
low  one.     In   1879,  Graham   Bell   and  Sumner  Tainter 
devised  "selenium   cells,"  in  which   annealed   selenium 
is  formed  into  narrow  strips  between  the  edges  of  broad 
conducting  plates  of  brass,  thus  securing  both  a  reduction 
of  the  transverse  resistance  and  a  large  amount  of  surface- 
exposure  to  light.     Thus  a  cell,  whose  resistance  in  the 
dark  was  300  ohms,  when  exposed   to  sunlight  had   a 
resistance  of  but  150  ohms.     This  property  of  selenium 
these  investigators  applied  in  the  construction  of  the  Pho- 
tophone,    an    instrument   which    transmits    sounds   to    a 
distance  by  means   of  a  beam  of  light  reflected   to  a 
distant  spot  from  a  thin  mirror  thrown  into  vibrations 
by    the    voice;    the    beam    falling,    consequently,    with 


572  ELECTRICITY  AND   MAGNETISM      PART  11 

varying  intensity  upon  a  receiver  of  selenium  connected 
in  circuit  with  a  small  battery  and  a  Bell  telephone 
receiver  (Art.  510)  in  which  the  sounds  are  reproduced 
by  the  variations  of  the  current. 

Similar  properties  are  possessed,  to  a  smaller  degree, 
by  tellurium.     Carbon  is  also  sensitive  to  light. 

530.  Photo-chemical   Cells.  —  About  the  middle  of 
the  present   century  Becquerel  showed  that  when  two 
plates  of  silver,  coated  with  freshly  deposited  chloride  of 
silver,  are  placed  in  a  cell  with  water  and  connected  with 
a  galvanometer,  a  current  is  observed  to  pass  when  light 
falls  upon  one  of  the  two  plates,  the  exposed  plate  acting 
as  an  anode ;  and  Minchin  has  more  recently  shown  the 
efficiency  of  other  photo-chemical  combinations.     Some 
of  these   are  very  sensitive  to  electric  waves  of  greater 
wave-length. 

531.  Photo-electric  Loss  of  Charge.  —  In  1887  Hertz 
made  the  discovery  that   a  spark   starts   more  readily 
between  the  balls  of  a  discharger  when  illuminated  by 
light  that  is  rich  in  violet  and  ultra-violet  rays  (magne- 
sium light,  arc  light,  or  spark  of  induction  coil)  than 
when  not  so  illuminated.     The  effect  varies  with  dif- 
ferent metals,  with  their  cleanness,  the  nature  of   the 
surrounding  gas,  with  the  kind  of  charge,  and  with  the 
polarization  of  the  light.     In  ultra-violet  light  freshly 
polished  zinc  in  air  rapidly  discharges  a  negative  charge, 
but  not  a  positive  one.     On  the  other  hand  the  peroxides, 
in    an   atmosphere    of    hydrogen,  when   so   illuminated 
readily  discharge  positive  charges.    The  effect  is  stronger 
when  the  plane  of  the  vibration  of  the  incident  waves  is 
at  right  angles  to  the  surface  than  when  the  polarization 
is  in  a  parallel  plane.     The  phenomenon  appears  to  be 
due  to  the   small  light-waves  stimulating  chemical  re- 
actions which  do  not  occur  except  (Art.  322)  by  a  species 
of  electric  exchange.     In  a  strong  magnetic  field  no  such 
discharges  occur.     Hallwachs  charged  clean  zinc  plates 
positively  by  exposure  to  ultra-violet  light. 


APPENDIX  A  — 


0  in 

Degrees. 

Bin 
Radians. 

Sine  e. 

Tangent  0. 

Solid  Angle 
2n-(l  —  cos0). 

Complement 
Of*»*. 

0° 

0 

0 

0 

0 

90° 

1 

•0175 

•0175 

•0175 

•000957 

89 

2 

•0349 

•0349 

•0349 

•003837 

88 

3 

•0524 

•0523 

•0524 

•00861 

87 

4 

•0698 

•0698 

•0699 

•01532 

86 

5 

•0873 

•0872 

•0875 

•02391 

85 

6 

•1047 

•1045 

•1051 

•03441 

84 

7 

•1222 

•1219 

•1228 

•04683 

83 

8 

•1396 

•1392 

•1405 

•06115 

82 

9 

•1571 

•1564 

•1584 

•07735 

81 

10 

•1745 

•1737 

•1763 

•09545 

80 

11 

•1920 

•1908 

•1944 

•1154 

79 

12 

•2094 

•2079 

•2126 

•1373 

78 

13 

•2269 

•2250 

•2309 

•1610 

77 

14 

•2444 

•2419 

•2493 

•1866 

76 

15 

•2618 

•2588 

•2680 

•2140 

75 

16 

•2793 

•2756 

•2868 

•2434 

74 

IT 

•2967 

•2924 

•3057 

•2745 

73 

18 

•3142 

•3090 

•3249 

•3075 

72 

19 

•3316 

•3256 

•3443 

•3423 

71 

20 

•3491 

•3420 

•3640 

•3789 

70 

21 

•3665 

•3584 

•3839 

•4173 

00 

22 

•3840 

•3746 

•4040 

•4575 

68 

23 

•4014 

•3907 

•4245 

•4994 

67 

24 

•4189 

•4067 

•4452 

•5431 

66 

25 

•4363 

•4226 

•4668 

•5886 

65 

26 

•4538 

•43,84 

•4877 

•6358 

64 

27 

•4712 

•4540 

•5095 

•6848 

63 

28 

•4887 

•4695 

•5317 

•7354 

62 

29 

•5062 

•4848 

•5543 

•7877 

61 

30 

•5236 

•5000 

•5774 

•8417 

60 

31 

•5411 

•5150 

•6009 

•8974 

59 

32 

•55S5 

•6299 

•6249 

•9507 

58 

33 

•5760 

•5446 

•6494 

1-0136 

57 

34 

•5934 

•8S92 

•6745 

1-0741 

56 

35 

•6109 

•5736 

•7002 

1-1362 

55 

36 

•6283 

•5878 

•7265 

1-1999 

54 

37 

•6458 

•6018 

•7536 

1-2652 

53 

38 

•6682 

•6157 

•7813 

1-3319 

52 

39 

•6807 

•6293 

•8098 

1-4002 

51 

40 

•6981 

•6428 

•8391 

1-4700 

50 

41 

•7156 

•6561 

•8693 

1-5412 

49 

42 

•7330 

•6691 

•9004 

1-6138 

48 

43 

•7505 

•6820 

•9325 

1-6879 

47 

44 

•7679 

•6947 

•9657 

1-7684 

46 

45 

•7854 

•7071 

i-oooo 

1-8402 

45 

Cosine  $ 

Cotangent  <$> 

27r(l  -  sin  $) 

<|>  in  Degrees 

574 


ANGLES   AND   SOLID   ANGLES 


0in 
Decrees. 

0in 

Radians. 

Sine  e. 

Tangent  0. 

Solid  Angle 

277(1  —  COS  0). 

Complement 
of0=4>. 

45° 

•7854 

•7071 

1-0000 

1-8402 

45° 

46 

•8029 

•7193 

1-0355 

1-9185 

44 

47 

•8203 

•7314 

1-0724 

1-9980 

43 

43 

•8378 

•7431 

1-1106 

2-0789 

42 

49 

•8552 

•7547 

1-1504 

2-1610 

41 

60 

•8727 

•7660 

1-1918 

2-2444 

40 

51 

•8901 

•7772 

1-2349 

2-3290 

39 

52 

•9076 

•7880 

1-2799 

2-4149 

38 

68 

•9250 

•7986 

1-3270 

2-5019 

37 

54 

•9425 

•8090 

1-3764 

2-5900 

36 

55 

•9599 

•8192 

1-4282 

2-6793 

35 

56 

•9774 

•8290 

1-4826 

2-7696 

34 

57 

•9948 

•8387 

1-5399 

2-8611 

33 

58 

•0123 

•8481 

1-6003 

2-9536 

32 

59 

•(1298 

•8572 

1-6643 

3-0472 

31 

GO 

1-0472 

•8660 

1-7321 

3-1416 

30 

61 

•0647 

•8746 

1-8041 

3-2370 

29 

62 

•0821 

•8830 

1-8807 

3-3334 

28 

63 

•0996 

•8910 

1-9626 

3-4307 

27 

64 

•1170 

•8988 

2-0503 

3-5288 

26 

65 

•1345 

•9063 

2-1445 

3-6278 

25 

66 

1-1519 

•9136 

2-2460 

3-7276 

24 

67 

•1694 

•9205 

2-3559 

3-8281 

23 

68 

1-1868 

•9272 

2-4751 

3-9295 

22 

69 

•2048 

•9336 

2-6051 

4-0315 

21 

70 

•2217 

•9397 

2-7475 

4-1342 

20 

71 

•2392 

•9455 

2-9042 

4-2376 

19 

'  2 

•2566 

•9511 

3-0777 

4-3416 

18 

3 

•2741 

•9563 

3-2709 

4-4462 

17 

4 

•2916 

•9613 

3-4S74 

4-5513 

16 

5 

•3090 

•9659 

3-7321 

4-6570 

15 

6 

•1-3265 

•9703 

4-0108 

4-7632 

14 

7 

•3439 

•9744 

4-3315 

4-8698 

13 

78 

•3614 

•9782 

4-7046 

4*9768 

12 

79 

•8788 

•9816 

5-1446 

5-0843 

11 

80 

•3963 

•9843 

5-6713 

5-1921 

10 

81 

1-4137 

•9877 

6-3138 

5-3003 

9 

82 

1-4312 

•9903 

7-1154 

5-4087 

8 

83 

1-4486 

•9926 

8-1444 

5-5174 

7 

84 

1-4661 

•9945 

9-5144 

5-6264 

6 

85 

1-4885 

•;»'.)•;•_' 

11-4301 

5-7356 

5 

86 

I'SOIO 

•9976 

14-3007 

5-8449 

4 

87 

1-5184 

•99S6 

19-0811 

5-9543 

3 

88 

1-58S9 

•9894 

28-6868 

6-0639 

2 

89 

1-5534 

•9909 

57-2900 

6-1735 

1 

91) 

1-5708 

1  '(Mil  III 

00 

6-2832 

0 

Cosine  tf» 

Cotangent  </> 

27r(l  -  sin  $) 

<t>  in  Degrees 

575 


APPENDIX   B 

[ABSTRACT  OF  BULLETIN  OF  U.  S.  COAST  AND  GEODETIC 
SURVEY,  DATED  DECEMBER  27,  1893] 

UNITS  OF  ELECTRICAL  MEASURE 

During  the  past  few  years  the  advance  of  knowledge  and 
experience  among  electricians  was  such  as  to  indicate  that  the 
time  was  ripe  for  the  general  adoption  of  the  principal  units  of 
electrical  measure.  An  International  Congress  of  Electricians 
was  aranged  for,  to  meet  in  Chicago,  during  the  World's  Colum- 
bian Exposition  of  1893.  In  this  Congress  the  business  of  denn- 
ing and  naming  units  of  measure  was  left  to  what  was  known 
as  the  "  Chamber  of  Delegates,"  a  body  composed  of  those  only 
who  had  been  officially  commissioned  by  their  respective  gov- 
ernments to  act  as  members  of  said  Chamber.  The  United 
States,  Great  Britain,  Germany,  and  France  were  each  allowed 
five  delegates  in  the  Chamber.  Other  nations  were  represented 
by  three,  two,  and  in  some  cases  one.  The  principal  nations  of 
the  world  were  represented  by  their  leading  electricians,  and 
the  Chamber  embraced  many  of  the  most  distinguished  living 
representatives  of  physical  science. 

The  delegates  representing  the  United  States  ha^  reported 
to  the  Honorable  the  Secretary  of  State,  under  date  of  Novem- 
ber 6,  1893,  giving  the  names  and  definitions  of  the  units  of 
electrical  measure  as  unanimously  recommended  by  the  Cham- 
ber in  a  resolution  as  follows : 

"Resolved,  That  the  several  governments  represented  by  the 
delegates  of  this  International  Congress  of  Electricians  be,  and 
they  are  hereby,  recommended  to  formally  adopt  as  legal  units 
of  electrical  measure  the  following:  As  a  unit  of  resistance, 
the  international  ohm,  which  is  based  upon  the  ohm  equal  to 
109  units  of  resistance  of  the  Centimetre-Gramme-Second  system 
of  electromagnetic  units,  and  is  represented  by  the  resistance 
offered  to  an  unvarying  electric  current  by  a  column  of  mercury 
at  the  temperatiire  of  melting  ice  14'4521  grammes  in  mass,  of 
a  constant  cross-sectional  area  and  of  the  length  of  1(X>'3  centi- 
metres. 

576 


APPENDIX  577 


"  As  a  unit  of  current,  the  international  ampere,  which  is  one- 
tenth  of  the  unit  of  current  of  the  C.G.S.  system  of  electro- 
magnetic units,  and  which  is  represented  sufficiently  well  for 
practical  use  by  the  unvarying  current  which,  when  passed 
through  a  solution  of  nitrate  of  silver  in  water,  and  in  accord- 
ance with  accompanying  specifications,*  deposits  silver  at  the 
rate  of  O'OOlllS  of  a  gramme  per  second. 

"  As  a  unit  of  electromotive-force,  the  international  volt, 
which  is  the  electromotive-force  that,  steadily  applied  to  a  con- 
ductor whose  resistance  is  one  international  ohm,  will  produce 
a  current  of  one  international  ampere,  and  which  is  represented 
sufficiently  well  for  practical  use  by  JS8J  of  the  electromotive- 
force  between  the  poles  or  electrodes  of  the  voltaic  cell  known 
as  Clark's  cell,  at  a  temperature  of  15°  C.,  and  prepared  in  the 
manner  described  in  the  accompanying  specification. f 

"  As  a  unit  of  quantity,  the  international  coulomb,  which  is 
the  quantity  of  electricity  transferred  by  a  current  of  one  in- 
ternational ampere  in  one  second. 

"  As  a  unit  of  capacity,  the  international  farad,  which  is  the 
capacity  of  a  condenser  charged  to  a  potential  of  one  interna- 
tional volt  by  one  international  coulomb  of  electricity. 

"  As  a  unit  of  work,  the  joule,  which  is  equal  to  1C7  units  of 
work  in  the  C.G.S.  system,  and  which  is  represented  sufficiently 


*  In  the  following  specification,  the  term  silver  voltameter  means  the 
arrangement  of  apparatus  by  means  of  which  an  electric  current  is  passed 
through  a  solution  of  nitrate  of  silver  in  water.  The  silver  voltameter 
measures  the  total  electrical  quantity  which  has  passed  during  the  time  of 
the  experiment,  and  by  noting  this  time,  the  time  average  of  the  current, 
or  if  the  current  has  been  kept  constant,  the  current  itself  can  be  deduced. 

In  employing  the  silver  voltameter  to  measure  currents  of  about  one 
ampere,  the  following  arrangements  should  be  adopted  : 

The  kathode  on  which  the  silver  is  to  be  deposited  should  take  the  form 
of  a  platinum  bowl,  not  less  than  10  centimetres  in  diameter  and  from  4  to 
5  centimetres  in  depth. 

The  anode  should  be  a  plate  of  pure  silver  some  30  square  centimetres 
in  area  and  2  or  3  millimetres  in  thickness. 

This  is  supported  horizontally  in  the  liquid  near  the  top  of  the  solution 
by  a  platinum  wire  passed  through  holes  in  the  plate  at  opposite  corners. 
To  prevent  the  disintegrated  silver  which  is  formed  on  the  anode  from 
falling  on  to  the  kathode,  the  anode  should  be  wrapped  round  with  pure  filter 
paper,  secured  at  the  back  with  sealing  wax. 

The  liquid  should  consist  of  a  neutral  solution  of  pure  silver  nitrate, 
containing  about  15  parts  by  weight  of  the  nitrate  to  85  parts  of  water. 

The  resistance  of  the  voltameter  changes  somewhat  as  the  current 
passes.  To  prevent  these  changes  having  too  great  an  effect  on  the  cur- 
rent, some  resistance  besides  that  of  the  voltameter  should  be  inserted  in 
the  circuit.  The  total  metallic  resistance  of  the  circuit  should  not  be  less 
than  10  ohms. 

t  A  committee,  consisting  of  Messrs.  Helmholtz,  Ayrton,  and  Carhart, 
was  appointed  to  prepare  specifications  for  the  Clark's  cell.  Their  report 
has  not  yet  been  received.  [It  is  substantially  identical  with  the  specifica- 
tion given  in  Appendix  C,  following,  which  is  that  adopted  by  the  British 
Board  of  Trade.] 

2p 


578  ELECTRICITY  AND   MAGNETISM 


well  for  practical  use  by  the  energy  expended  in  one  second  by 
an  international  ampere  in  an  international  ohm. 

"  As  a  unit  of  power,  the  watt,  which  is  equal  to  10"  units 
of  power  in  the  C.G.S.  system,  and  which  is  represented  suffi- 
ciently well  for  practical  work  done  at  the  rate  of  one  joule 
per  second. 

"  As  the  unit  of  induction,  the  henry,  which  is  the  induction 
in  a  circuit  when  the  electromotive-force  induced  in  this  circuit 
is  one  international  volt,  while  the  inducing  current  varies  at 
the  rate  of  one  ampere  per  second." 

To  make  the  use  of  these  units  obligatory  in  all  parts  of  the 
country  will  require  an  act  of  Congress,  but  in  the  absence  of 
that,  it  is  within  the  power  of  the  Secretary  of  the  Treasury 
to  approve  their  adoption  for  use  in  all  Departments  of  the  Gov- 
ernment. This,  indeed,  is  precisely  the  course  long  ago  followed 
in  reference  to  the  ordinary  weights  and  measures  of  commerce 
and  trade.  Congress  has  "never  enacted  a  law  fixing  the  value 
of  their  units,  but  the  Secretary  of  the  Treasury  was  authorized 
to  establish  and  construct  standards  for  use  in  the  various 
Departments  of  the  Government.  Uniformity  has  followed  on 
account  of  the  universal  adoption  of  these  standards  by  the 
several  States. 

The  Government  is  itself  a  large  consumer  of  electricity  and 
electrical  machinery,  and  for  its  own  protection  it  is  impoi'tant 
that  units  of  measure  be  adopted.  With  the  approval,  there- 
fore, of  the  Honorable  the  Secretary  of  the  Treasury,  the  formal 
adoption  by  the  Office  of  Standard  Weights  and  Measures  of 
the  names  and  values  of  units  of  electrical  measure  as  given 
above,  the  same  being  in  accord  with  the  recommendations  of 
the  International  Congress  of  Electricians  of  1893,  is  hereby 
announced. 

T.  C.  MENDENHALL, 
Superintendent  U.  S.  Coast  and  Geodetic  Survey, 

and  of  Standard  Weights  and  Measures. 
Approved : 

J.  G.  CARLISLE, 

Secretary  of  the  Treasury. 


APPENDIX  C 


OFFICIAL  SPECIFICATION  FOB  THE  PREPARATION  OF  THE 
CLARK  CELL 

Definition  of  the  Cell 

The  cell  consists  of  zinc  or  an  amalgam  of  zinc  with  mer- 
cury and  of  mercury  in  a  neutral  saturated  solution  of  zinc 
sulphate  and  mercurous  sulphate  in  water,  prepared  with 
mercurous  sulphate  in  excess. 

Preparation  of  the  Materials 

1.  The  Mercury.  —  To  secure  purity  it  should  be  first  treated 
with  acid  in  the  usual  manner,  and  subsequently  distilled  in 
vacuo. 

2.  The  Zinc.  — Take  a  portion  of  a  rod  of  pure  redistilled  zinc, 
solder  to  one  end  a  piece  of  copper  wire,  clean  the  whole  with 
glass  paper  or  a  steel  burnisher,  carefully  removing  any  loose 
pieces  of  the  zinc.    Just  before  making  up  the  cell  dip  the  zinc 
into  dilute  sulphuric  acid,  wash  with  distilled  water,  and  dry 
with  a  clean  cloth  or  filter  paper. 

3.  The    Mercurous    Sulphate.  —  Take    mercurous    sulphate, 
purchased  as  pure,  mix  with  it  a  small  quantity  of  pure  mer- 
cury, and  wash  the  whole  thoroughly  with  cold  distilled  water 
by  agitation  in  a  bottle;    drain  off  the  water,  and  repeat  the 
process  at  least  twice.      After  the  last  washing,  drain  off  as 
much  of  the  water  as  possible. 

4.  The   Zinc  Sulphate  Solution.  — Prepare  a  neutral  satu- 
rated solution  of  pure  ("  pure  recrystallized  ")  zinc  sulphate  by 
mixing  in  a  flask  distilled  water  with  nearly  twice  its  weight 
of  crystals  of  pure  zinc  sulphate,  and  adding  zinc  oxide  in  the 
proportion  of  about  2  per  cent  by  weight  of  the  zinc  sulphate 
crystals  to  neutralize  any  free  acid.     The  crystals  should  be 

679 


580  ELECTRICITY    AND   MAGNETISM 


dissolved  with  the  aid  of  gentle  heat,  but  the  temperature  to 
which  the  solution  is  raised  should  not  exceed  30°  C.  Mer- 
curous  sulphate  treated  as  described  in  3  should  be  added  in 
the  proportion  of  about  12  per  cent  by  weight  of  the  zinc  sul- 
phate crystals  to  neutralize  any  free  zinc  oxide  remaining,  and 
the  solution  filtered,  while  still  warm,  into  a  stock  bottle.  Crys- 
tals should  form  as  it  cools. 

5.  The  Mercurous  Sulphate  and  Zinc  Sulphate  Paste.  —  Mix 
the  washed  mercurous  sulphate  with  the  zinc  sulphate  solu- 
tion, adding  sufficient  crystals  of  zinc  sulphate  from  the  stock 
bottle  to  ensure  saturation,  and  a  small  quantity  of  pure  mer- 
cury. Shake  these  up  well  together  to  form  a  paste  of  the 
consistence  of  cream.  Heat  the  paste,  but  not  above  a  tem- 
perature of  30°  C.  Keep  the  paste  for  an  hour  at  this  temper- 
ature, agitating  it  from  time  to  time,  then  allow  it  to  cool ; 
continue  to  shake  it  occasionally  vyhile  it  is  cooling.  Crystals 
of  zinc  sulphate  should  then  be  distinctly  visible,  and  should 
be  distributed  throughout  the  mass;  if  this  is  not  the  case 
add  more  crystals  from  the  stock  bottle,  and  repeat  the  whole 
process. 

This  method  ensures  the  formation  of  a  saturated  solution  of 
zinc  and  mercurous  sulphates  in  water. 

To  set  up  the  Cell 

The  cell  may  conveniently  be  set  up  in  a  small  test  tube  of 
about  2  centimetres  diameter,  and  4  or  5  centimetres  deep. 
Place  the  mercury  in  the  bottom  of  this  tube,  filling  it  to  a 
depth  of  say  0'5  centimetre.  Cut  a  cork  about  0'5  centimetre 
thick  to  fit  the  tube ;  at  one  side  of  the  cork  bore  a  hole  through 
which  the  zinc  rod  can  pass  tightly;  at  the  other  side  bore 
another  hole  for  the  glass  tube  which  covers  the  platinum  wire ; 
at  the  edge  of  the  cork  cut  a  nick  through  which  the  air  can 
pass  when  the  cork  is  pushed  into  the  tube.  Wash  the  cork 
thoroughly  with  warm  water,  and  leave  it  to  soak  in  water  for 
some  hours  before  use.  Pass  the  zinc  rod  about  1  centimetre 
through  the  cork. 

Contact  is  made  with  the  mercury  by  means  of  a  platinum 
wire  about  No.  22  gauge.  This  is  protected  from  contact 
with  the  other  materials  of  the  cell  by  being  sealed  into  a 
glass  tube.  The  ends  of  the  wire  project  from  the  ends  of  the 
tube ;  one  end  forms  the  terminal,  the  other  end  and  a  portion 
of  the  glass  tube  dip  into  the  mercury. 

Clean  the  glass  tube  and  platinum  wire  carefully,  then 
heat  the  exposed  end  of  the  platinum  red  hot,  and  insert  it  in 
the  mercury  in  the  test  tube,  taking  care  that  the  whole  of 
the  exposed  platinum  is  covered. 

Shake  up  the  paste  and  introduce  it  without  contact  with 
the  upper  part  of  the  walls  of  the  test  tube,  filling  the  tube 
above  the  mercury  to  a  depth  of  rather  more  than  1  centi- 
metre, 


APPENDIX  581 


Then  insert  the  cork  and  zinc  rod,  passing  the  glass  tube 
through  the  hole  prepared  for  it.  Push  the  cork  gently  down 
until  its  lower  surface  is  nearly  in  contact  with  the  liquid. 
The  air  will  thus  be  nearly  all  expelled,  and  the  cell  should 
be  left  in  this  condition  for  at  least  24  hours  before  sealing, 
which  should  be  done  as  follows  : 

Melt  some  marine  glue  until  it  is  fluid  enough  to  pour  by 
its  own  weight,  and  pour  it  into  the  test  tube  above  the  cork, 
using  sufficient  to  cover  completely  the  zinc  and  soldering.  The 
glass  tube  containing  the  platinum  wire  should  project  some 
way  above  the  top  of  the  marine  glue. 

The  cell  may  be  sealed  in  a  more  permanent  manner  by  coat- 
ing the  marine  glue,  when  it  is  set,  with  a  solution  of  sodium 
silicate,  and  leaving  it  to  harden. 

The  cell  thus  set  up  may  be  mounted  in  any  desirable 
manner.  It  is  convenient  to  arrange  the  mounting  so  that 
the  cell  may  be  immersed  in  a  water  bath  up  to  the  level  of, 
say,  the  upper  surface  of  the  cork.  Its  temperature  can  then 
be  determined  more  accurately  than  is  possible  when  the  cell  is 
in  air. 

In  using  the  cell  sudden  variations  of  temperature  should  as 
far  as  possible  be  avoided. 

The  form  of  the  vessel  containing  the  cell  may  be  varied.  In 
the  H-form,  the  zinc  is  replaced  by  an  amalgam  of  10  parts  by 
weight  of  zinc  to  90  of  mercury.  The  other  materials  should  be 
prepared  as  already  described.  Contact  is  made  with  the  amal- 
gam in  one  leg  of  the  cell,  and  with  the  mercury  in  the  other, 
by  means  of  platinum  wires  sealed  through  the  glass. 


PROBLEMS  AND  EXERCISES 


QUESTIONS    ON    CHAPTER    I 

1.  In  what  respects  does  an  electrified  body  differ  from  a 
non-electrified  body  ? 

2.  Name  some  of  the  different  methods  of  producing  electri- 
fication. 

3.  A  body  is  charged  so  feebly  that  its  electrification  will 
not  perceptibly  move  the  leaves  of  a  gold-leaf  electroscope. 
Can  you  suggest  any  means  of  ascertaining  whether  the  charge 
of  the  body  is  positive  or  negative  ? 

4.  How  would  you  prove  that  the  production  of  a  positive 
charge  is  accompanied  by  the  production  of  an  equal  negative 
charge  ? 

5.  Describe  an  experiment  to  prove  that  moistened  thread 
conducts  electricity  better  than  dry  thread. 

6.  Why  do  we  regard  the  two  electric  charges  produced 
simultaneously  by  rubbing  two  bodies  together  as  being  of 
opposite  kinds? 

7.  Explain  the  action  of  the  electrophorus.      Can  you  sug- 
gest any  means  for  accomplishing  by  a  rotatory  motion  the 
operations  of  lifting  up  and  down  the  cover  of  the  instrument 
so  as  to  obtain  a  continuous  supply  instead  of  an  intermittent 
one? 

8.  Describe  the  state  of  the  medium  between  two  oppositely 
charged  bodies,  and  state  how  you  would  determine  the  direc- 
tion of  the  lines  of  force  at  any  point. 

9.  Explain  the  Torsion  Balance,  and  how  it  can  be  used  to 
investigate  the  laws  of  the  distribution  of  electricity. 

10.  Describe  what  takes  place  as  an  electrified  conducting 
ball  is  made  to  approach  a  large  conducting  surface.    Show  by 
diagram  the  direction  and  relative  number  of  the  lines  of  force. 

682 


PROBLEMS   AND   EXERCISES  583 


11 .  Two  small  balls  are  charged  respectively  with  -\-  24  and 
—  8  units  of  electricity.    With  what  force  will  they  attract  one 
another  when  placed  at  a  distance  of  4  centimetres  from  one 
another?  Ans.  12  dynes. 

12.  If  these  two  balls  are  then  made  to  touch  for  an  instant 
and  then  put  back  in  their  former  positions,  with  what  force 
will  they  act  on  each  other  ? 

Ans.  They  will  repel  one  another  with  a  force  of  4  dynes. 

13.  Enumerate  the  essential  parts  of  an  influence  machine ; 
and  explain  how  they  operate  to  produce  electrification. 

14.  Take  the  diagrammatic  representation  of  the  Wimshurst 
machine  (Fig.  40)  and  fill  in  the  lines  of  electric  force,  showing 
their  direction  and  relative  number. 

15.  Explain  the  action  of  the  Leyden  jar  by  the  consideration 
of  electric  displacement. 

1C.  Describe  four  different  ways  of  electrifying  a  tourmaline 
crystal. 

17.  Zinc  filings  are  sifted  through  a  sieve  made  of  copper 
wire  upon  an  insulated  zinc  plate  joined  by  a  wire  to  an  electro- 
scope.   What  will  be  observed  ? 

18.  Explain  the  principle  of  an  air-condenser ;  and  state  why 
it  is  that  the  two  oppositely  charged  plates  show  less  signs  of 
electrification  when  placed  near  together  than  when  drawn  apart 
from  one  another. 

19.  There  are  four  Leyden  jars  A,  B,  C,  and  D,  of  which  A, 
B,  and  D  are  of  glass,  C  of  guttapercha.     A,  B,  and  C  are  of  the 
same  size,  D  being  just  twice  as  tall  and  twice  as  wide  as  the 
others.    A,  C,  and  D  are  of  the  same  thickness  of  material, 
but  B  is  made  of  glass  only  half  as  thick  as  A  or  D.    Compare 
their  capacities. 

Ans.  Take  capacity  of  A  as  1 ;  that  of  B  will  be  2 ;  that 
of  C  will  be  I ;  and  that  of  D  will  be  4. 

20.  How  would  you  show  that  a  bar  made  half  of  zinc  and 
half  of  copper  is  capable  of  producing  electrification  ? 

21.  How  would  you  prove  that  there  is  no  electrification 
within  a  closed  conductor  ? 

22.  What  prevents  the  charge  of  a  body  from  escaping  away 
at  its  surface  ? 

23.  Explain  the  action  of  Hamilton's  mill. 

24.  Two  brass  balls  mounted  on  glass  stems  are  placed  half 
an  inch  apart.    One  of  them  is  gradually  charged  by  a  machine 
until  a  spark  passes  between  the  two  balls.     State  exactly  what 
happened  in  the  other  brass  ball  and  in  the  intervening  air  up 
to  the  moment  of  the  appearance  of  the  spark. 


584  ELECTRICITY   AND   MAGNETISM 


25.  Define  electric  density.  A  charge  of  248  units  of  elec- 
tricity was  imparted  to  a  sphere  of  4  centimetres  radius.  What 
is  the  density  of  the  charge?  Ans.  l'2'3  (nearly). 


QUESTIONS  ON  CHAPTER  II 

1.  A  dozen    steel  sewing-needles  are  hung  in  a  bunch  by 
threads  through  their  eyes.     How  will  they  behave  when  hung 
over  the  pole  of  a  strong  magnet? 

2.  Explain  the  operation  of  an  iron  screen  in  protecting  a 
galvanometer  needle  from  magnets  in  its  vicinity,   and  state 
why  it  is  not  perfectly  effectual. 

3.  Of  what  material,  and  of  what  shape,  would  you  make  a 
magnet  which  is  required  to  preserve  its  magnetism  unaltered 
for  a  very  long  time  ?    Describe  the  process  of  tempering. 

4.  What  is  meant    by  the  resultant   magnetic  force  at  a 
point? 

5.  Six    magnetized    sewing-needles    are     thrust    vertically 
through  six  little  floats  of  cork,  and  are  placed  in  a  basin  of 
water  with  their  N-pointing  poles  upwards.      How  will  they 
affect  one  another,  and  what  will  be  the  effect  of  holding  over 
them  the  S-pointiug  pole  of  a  magnet? 

6.  What  distinction  do  you  draw  between  magnets  and  mag- 
netic matter  ? 

7.  On  board  an  iron  ship  which  is  laying  a  submarine  tele- 
graph cable  there  is  a  galvanometer  used  for  testing  the  conti- 
nuity of  the  cable.    It  is  necessary  to  screen  the  magnetized 
needle  of  the  galvanometer  from  being  affected  by  the  magnetism 
of  the  ship.    How  can  this  be  done  ? 

8.  How   would    you    prove    two    magnets    to   be   of   equal 
strength? 

9.  The  force  which  a  magnet-pole  exerts  upon  another  magnet- 
pole  decreases  as  you  increase  the  distance  between  them.    What 
is  the  exact  law  of  the  magnetic  force,  and  how  is  it  proved 
experimentally  ? 

10.  Describe  the  behaviour  of  Ewing's  model  of  molecular 
magnetism  in  a  magnetic  field,  and  show  how  it  corresponds 
with  the  behaviour  of  iron  when  magnetized.    Divide  the  process 
of  magnetizing  into  three  successive  stages. 

11.  What  force  does  a  magnet-pole,  the  strength  of  which  is 
9  units,  exert  upon  a  pole  whose  strength  is  10  units  placed  0 
centimetres  away  ?  Ans.  4  dynes. 


PROBLEMS   AND   EXERCISES  585 


12.  How  would  you  place  a  long  magnet  so  that  one  of  its 
poles  deflects  a  compass  while  the  other  does  not  affect  it  ? 

13.  Distinguish  hetween  the  "  strength"  of  a  magnet  and  its 
"  magnetic  moment." 

14.  Describe    an    instrument    for    comparing    the    relative 
values  of  magnetic  forces.    How  would  you  use  it  to  compare 
the  magnetic  moments  of  two  magnets?     If  their  distances 
from  the  magnetometer  are  respectively  20  centimetres  and  30 
centimetres,  what  is  the  ratio  of  their  magnetic  moments  ? 

Ans.  8 : 27. 

15.  Two  magnets  have  the  same  pole  strength,  but  one  is  twice 
as  long  as  the  other.    The  shorter  is  placed  20  centimetres  from 
a  magnetometer  (using  the  end-on  method) ;  state  at  what  dis- 
tance the  other  must  be  placed  in  order  that  there  may  be  no 
deflexion.  Ans.  25'2  centimetres. 

1(5.  A  pole  of  strength  40  units  acts  with  a  force  of  32  dynes 
upon  another  pole  5  centimetres  away.  What  is  the  strength  of 
that  pole?  Ans.  20  units. 

17.  It  is  desired  to  compare  the  magnetic  force  at  a  point  10 
centimetres  from  the  pole  of  a  magnet  with  the  magnetic  force 
at  5  centimetres'  distance.    Describe  four  ways  of  doing  this. 

18.  Explain  the  phenomenon  of  Consequent  Poles. 

19.  In  what  direction  do   the  lines  of   magnetic  induction 
(or  "  lines  of  force  ")  run  in  a  plane  in  which  there  is  a  single 
magnetic  pole?     How  would   you  arrange  an  experiment  by 
which  to  test  your  answer  ? 

20.  What  is  a  Magnetic  Shell  ?  What  is  the  law  of  the  poten- 
tial due  to  a  magnetic  shell  ? 

21.  A  steel  bar  magnet  suspended   horizontally,  and  set  to 
oscillate  at    Bristol,   made    110  complete  oscillations  in  five 
minutes ;  the  same  needle  when  set  oscillating  horizontally  at 
St.  Helena  executed  112  complete  oscillations  in  four  minutes. 
Compare  the  horizontal  component  of  the  force  of  the  earth's 
magnetism  at  Bristol  with  that  at  St.  Helena. 

Ans.  H  at  Bristol :  H  at  St.  Helena :  :  484 :  784. 

22.  Supposing  the  dip  at  Bristol  to  be  70°  and  that  at  St. 
Helena  to  be   30°,  calculate  from  the  data  of  the  preceding 
question  the  total  force  of  the  earth's  magnetism  at  St.  Helena, 
that  at  Bristol  being  taken  as  0'48  unit.  Ans.  0'307. 

23.  A  small  magnetic  needle  was  placed  magnetically  north 
of  the  middle  point  of  a  strong  bar-magnet  which  lay  (magneti- 
cally) east  and  west.    When  the  magnet  was  3  feet  away  from 
the  needle  the  deflexion  of  the  latter  was  2° :  when  moved  up 


58G  ELECTRICITY   AND   MAGNETISM 


to  a  distance  of  2  feet  the  deflexion  was  6D  30' ;  and  when  only  1 
foot  apart  the  deflexion  was  43°.  Deduce  the  law  of  the  total 
action  of  one  magnet  on  another. 

24.  Describe  how  the  daily  irregularities  of  the  earth's  mag- 
netism are  registered  at  different  stations  for  comparison. 


QUESTIONS  ON  CHAPTER  III 

1.  Show  that  the  total  of  the  differences  of  potential  by  con- 
tact in  three  simple  voltaic  cells  joined  in  series  is  three  times 
as  great  as  the  difference  of  potential  in  one  cell,  the  materials 
being  the  same  in  each. 

2.  Classify  the  different  methods  of  preventing  polarization 
in  voltaic  cells,  and  state  the  advantages  and  disadvantages  of 
using  a  strong  depolarizer,  such  as  chromic  acid. 

3.  On  what  does  the  internal  resistance  of  a  battery  depend  ? 
Is  there  any  way  of  diminishing  it? 

4.  A  current  of  10  amperes  flows  for  half  an  hour ;  find  the 
total  quantity  of  electricity  that  passes.      Also  define  the  unit 
by  which  the  quantity  is  measured.  Ans.  18,000  coulomb*. 

5.  State  from  what  source  the  energy  yielded  by  a  voltaic 
cell  is  derived. 

6.  How  is  local  action  in  a  voltaic  cell  minimized  ? 

7.  Twenty-four  similar   cells  are  grouped  together  in  four 
rows  of  six  cells  each;  compare   the  electromotive-force  and 
the  resistance  of  the  battery  thus  grouped,  with  the  electro- 
motive-force and  the  resistance  of  a  single  cell. 

Ans.  The  E.M.F.  of  the  battery  is  six  times  that  of  one 
cell.  The  total  internal  resistance  is  one  and  a  half 
times  that  of  one  cell. 

8.  Describe  a  form  of  cell  that  could  be  used  as  a  standard 
of  E.M.F.     State  the  essential  qualities  of  such  a  cell. 

9.  A  piece  of  silk-covered    copper  wire  is  coiled  round  the 
equator  of  a  model  terrestrial  globe.    Apply  Ampere's  rule  to 
determine  in  which  direction  a  current  must  be  sent  through 
the  coil  in  order  that  the  model  globe  may  represent  the  condi- 
tion of  the  earth  magnetically. 

Ans.  The  current  must  flow  across  the  Atlantic  from 
Africa  to  America,  and  across  the  Pacific  from 
America  toward  India ;  or,  in  other  words,  must  flow 
always  from  east  toward  west. 

10.  A  current  of  '24  amperes  flows  through  a  circular  coil  of 
seventy-two  turns,  the  (average)  diameter  of  the  coils  being  20 
centimetres.    What  is  the  strength  of  the  magnetic  field  which 
the  current  produces  at  the  centre  of  the  coil?  Ans.  1*08. 


PROBLEMS  AND  EXERCISES  587 


11.  Show  the  direction  of  the  lines  of  force  about  a  conductor 
carrying  a  current  (1)  when  the  conductor  is  straight ;  (2)  when 
it  is  bent  into  the  form  of  a  ring ;  (3)  when  it  is  wound  on  a 
cylinder  many  times  round.    What  do  you  mean  by  the  direction 
of  the  lines  of  force  ? 

12.  Suppose  a  current  passing  through  the  above  coil  pro- 
duced a  deflexion  of  35°  upon  a  small  magnetic  needle  placed 
at  its  centre  (the  plane  of  the  coils  being  in  the  magnetic  meri- 
dian), at  a  place  where  the  horizontal  component  of  the  earth's 
magnetic  force  is  '23  units.     Calculate  the  strength  of  the  current 
in  amperes.     (Art.  213.)  Ans.  0-035. 

13.  The  current  generated  by  a  dynamo-electric  machine  was 
passed  through  a  large  ring  of  stout  copper  wire,  at  the  centre 
of  which  hung  a  small  magnetic  needle  to  serve  as  a  tangent 
galvanometer.    When  the  steam  engine  drove  the  armature  of 
the  generator  at  450  revolutions  per  minute  the  deflexion  of  the 
needle  was  (KP.     When  the  speed  of  the  engine  was  increased 
so  as  to  produce  900  revolutions  per  minute  the  deflexion  was 
74°.    Compare  the  strength  of  the  currents  in  the  two  cases. 

Ans.   The  current  was  twice  as  great  as  before,  for 
tan  74°  is  almost  exactly  double  of  tan  GO3. 

14.  State  a  general  law  which  will  enable  you  to  find  the 
way  in  which  the  different  parts  of  a  magnetic  system  tend  to 
move. 

15.  Deduce  the  law  of  the  force  on  a  magnetic  pole  due  to 
a  current  flowing  along  a  long  straight  conductor. 

16.  Describe    four    ways    of   controlling   the    needle  of    a 
galvanometer. 

17.  What  is  meant  by  a  "  null  method  "  of  observation  ? 

18.  Why  is  the  needle  of  a  tangent  galvanometer  made  very 
short? 

19.  You  are  supplied  with  an  ammeter  and  a  voltmeter  for 
the  purpose  of  ascertaining  the  current  supplied  to  an  electro- 
lytic bath,  and  the  voltage  at  which  it  is  supplied.     Show  how 
you  would  join  them  up. 

20.  The  current  from  two  Grove's  cells  was  passed  through 
a  sine-galvanometer  to  measure  its  strength.    When  the  con- 
ducting wires  were  of   stout  copper  wire  the  coils  had  to  be 
turned  through  70°  before  they  stood  parallel  to  the  needle. 
But  when  long  thin  wires  were  used  as  conductors  the  coils  only 
required  to  be  turned  through  9°.    Compare  the  strength  of 
the  current  in  the  first  case  with  that  in  the  second  case  when 
flowing   through    the    thin  wires  which  offered   considerable 
resistance.  Ans.  Currents  are  as  1  to  $,  or  as  6  to  1. 


588  ELECTRICITY   AND   MAGNETISM 


21.  A  plate  of  zinc  and  a  plate  of  copper  are  respectively 
united  by  copper  wires  to  the  two  screws  of  a  galvanometer. 
They  were  then  dipped  side  by  side  into  a  glass  containing 
dilute  sulphuric  acid.    The  galvanometer  needle  at  first  showed 
a  deflexion   of  28°,  but  five  minutes  later  the  deflexion  had 
fallen  to  11°.    How  do  you  account  for  this  falling  off  ? 

22.  Classify  liquids  according  to  their  power  of  conducting 
electricity.    In  which  class  would  melted  pewter  come  ? 

23.  Name  the  substances  produced  at  the  anode  and  kathode 
respectively  during  the  electrolysis  of  the  following  substances : 
—  Water,  dilute  sulphuric  acid,  sulphate  of  copper  (dissolved 
in  water),  hydrochloric  acid  (strong),  iodide  of  potassium  (dis- 
solved in  water) ,  chloride  of  tin  (fused) . 

24.  A  current  is  sent  through  three  electrolytic  cells,  the 
first  containing  acidulated  water,  the  second  sulphate  of  copper, 
the  third  contains  a  solution  of  silver  in  cyanide  of  potassium. 
How  much  copper  will  have  been  deposited  in  the  second  cell 
while  2'2<>8  grammes  of  silver  have  been  deposited  in  the  third 
cell  ?    And  what  volume  of  mixed  gases  will  have  been  given  off 
at  the  same  time  in  the  first  cell  ? 

Am.  -6656  grammes  of  copper  and  351-4  cubic  centi- 
metres of  mixed  gases. 

25.  A  current  passes  by  platinum  electrodes  through  three 
cells,  the  first  containing  a  solution  of  blue  vitriol  (cupric  sul- 
phate), the  second  containing  a  solution  of  green  vitriol  (ferrous 
sulphate),  the  third  containing  a  solution  of  ferric  chloride. 
State  the  amounts  of  the  different  substances  evolved  at  each 
electrode  by  the  passage  of  1000  coulombs  of  electricity. 

,„„    v-r,f  ^77   (  Anode  '0829  gramme  of  oxygen  gas. 

eii'  \  Kathode  -3281  gramme  of  copper, 
o        ^  n  77  (  Anode  '0829  gramme  of  oxygen. 
Second  Cell,  j  Kathode  ^g  gramme  Of  ir§n. 

T?  •  /i  n  77  I  Anode  '3073  gramme  of  chlorine. 
9  Oe"'  j  Kathode  -1935  gramme  of  iron. 

26.  The  ends  of  a  coil  of  fine  insulated  wire  are  connected 
with  the  terminals  of  a  galvanometer.    A  steel  bar  magnet  is 
pushed  slowly  into  the  hollow  of  the  coil  and  then  withdrawn 
suddenly.    What  actions  will  be  observed  on  the  needle  of  the 
galvanometer  ? 

27.  Round  the  outside  of  a  deep  cylindrical  jar  are  coiled 
two  separate  pieces  of  fine  silk-covered  wire,  each  consisting  of 
many  turns.    The  ends  of  one  coil  are  fastened  to  a  battery, 
those  of  the  other  to  a  sensitive  galvanometer.    When  an  iron 
bar  is  poked  into  the  jar  a  momentary  current  is  observed  in  the 
galvanometer  coils,  and  when  it  is  drawn  out  another  momen- 
tary current,  but  in  an  opposite  direction,  is  observed.    Explain 
these  observations. 


PROBLEMS   AND   EXERCISES  589 


28.  A  casement  window  has  an  iron  frame.    The  aspect  is 
north,  the  hinges  being  on  the  east  side.     What  happens  in  the 
frame  when  the  window  is  opened  ? 

29.  Explain  the  construction  of  the  induction  coil.    What  are 
the  particular  uses  of  the  condenser,  the  automatic  hreak,  and 
the  iron  wire  core? 

30.  It  is  desired  to  measure  the  strength  of  the  field  between 
the  poles  of  an  electromagnet  which  is  excited  by  a  current 
from  a  constant  source.     How  could  you  apply  Faraday's  dis- 
covery of  induction-currents  to  this  purpose  ? 

31.  A  small  battery  was  joined  in  circuit  with  a  coil  of  fine 
wire  and  a  galvanometer,  in  which  the  current  was  found  to 
produce  a  steady  but  small  deflexion.    An  unmagnetized  iron 
bar  was  now  plunged  into  the  hollow  of  the  coil  and  then 
withdrawn.    The  galvanometer  needle  was  observed  to  recede 
momentarily  from  its  first  position,   then  to  return   and   to 
swing  beyond  it  with  a  wider  arc  than  before,  and  finally  to 
settle  down  to  its  original  deflexion.     Explain  these  actions, 
and  state  what  was  the  source  of  the  energy  that  moved  the 
needle. 

32.  A  tangent  galvanometer,  whose  "constant"  in  absolute 
units  was  0'08  was  joined  in  circuit  with  a  battery  and  an 
electrolytic  cell  containing  a  solution  of  silver.     The  current 
was  kept  on  for  one  hour;    the    deflexion    observed    at    the 
beginning  was  36°,  but  it  fell  steadily  during  the  hour  to  34°. 
Supposing  the  horizontal  component  of  the  earth's  magnetic 
force  to  be  '23,  calculate  the  amount  of  silver  deposited  in  the 
cell  during  the  hour,  the  absolute  electro-chemical  equivalent  of 
silver  being  0'01134.  Am.  0'526  gramme. 

33.  A  piece  of  zinc,  at  the  lower  end  of  which  a  piece  of 
copper  wire  is  fixed,  is  suspended  in  a  glass  jar  containing  a 
solution  of  acetate  of  lead.     After  a  few  hours  a  deposit  of  lead 
in  a  curious  tree-like  form  ("Arbor  Saturni")  grows  downwards 
from  the  copper  wire.    Explain  this. 

34.  Explain  the  conditions  under  which  electricity  excites 
muscular  contraction.     How  can  the  converse  phenomenon  of 
currents  of  electricity  produced  by  muscular  contraction  be 
shown  ? 

35.  A  certain  piece  of  apparatus  has  two  terminals  on  each 
side.    To  these  a  pair  of  wires,, A  and  B,  are  attached  at  one 
side,  and  another  pair  at  C  and  D.    Examination  with  a  volt- 
meter shows  that  the  potential  of  A  is  higher  than  that  of  B, 
and  that  of  C  higher  than  that  of  D.    Yet  examination  with  an 
ampere-meter  shows  that  a  current  is  flowing  from  B  to  A 
through    the    apparatus,   and    another    current    from  C  to  D 
through  the  other  part  of  the  apparatus.    By  which  circuit  is 
the  energy  coming  in,  and  by  which  is  it  going  out  ? 


590  ELECTRICITY   AND   MAGNETISM 


36.  Show  that  if  N  magnetic  lines  are  withdrawn  from  a  cir- 
cuit of  resistance  R,  the  quantity  of  electricity  thereby  trans- 
ferred around  the  circuit  (i.e.  the  time  integral  of  the  induced 
current)  will  be  Q  =  N/R.     (See  Art.  225.) 

37.  The  strength  of  the  field  between  the  poles  of  a  large 
electromagnet  was  determined  by  the  following  means :  —  A 
small  circular  coil,  consisting  of  40  turns  of  fine  insulated  wire, 
mounted  on  a  handle,  was  connected  to  the  terminals  of  a 
long-coil  galvanometer  having  a  heavy  needle.     On  inverting 
this  coil  suddenly,  at  a  place  where  the  total  intensity  of  the 
earth's  magnetic  force  was  '48  unit,  a  deflexion  of  6°  was  shown 
as  the  first  swing  of  the  galvanometer  needle.    The  sensitiveness 
of  the  galvanometer  was  then  reduced  to  TOO  by  means  of  a 
shunt.    The  little  coil  was  introduced  between  the  poles  of  the 
electromagnet  and  suddenly  inverted,  when  the  first  swing  of 
the  galvanometer  needle  reached  40°.    What  was  the  strength 
of  the  field  between  the  poles?  Ans.  315'7  units. 

QUESTIONS  ON  CHAPTER  IV 

1.  Define  the  unit  of  electricity  as  derived  in  absolute  terms 
from  the  fundamental  units  of  length,  mas*,  and  time. 

2.  At  what  distance  must  a  small  sphere  charged  with  28 
units  of  electricity  be  placed  from  a  second  sphere  charged  with 
56  units  in  order  to  repel  the  latter  with  a  force  of  32  dynes  ? 

Ans.  1  centimetres. 

3.  Suppose  the  distance  from  the  earth  to  the  moon  to  be  (in 
round  numbers)  383  X  108  centimetres;  and  that  the  radius  of 
the  earth  is  66  X  107  centimetres,  and  that  of  the  moon  15  X  107 
centimetres ;  and  that  both  moon  and  earth  are  charged  until 
the  surface  density  on  each  of  them  is  of  the  average  value  of 
10  units  per  square  centimetre.    Calculate  the  electrostatic  re- 
pulsion between  the  moon  and  the  earth. 

4.  A  small  sphere  is  electrified  with  24  units  of  +  electricity. 
Calculate  the  force  with  which  it  repels  a  unit  of  +  electricity 
at  distances  of  1,  2,  3,  4,  5,  6,  8,  and  10  centimetres  respectively. 
Then  plot  out  the  "  curve  of  force"  to  scale;   measuring  the 
respective  distances  along  a  line  from  left  to  right  as  so  many 
centimetres  from  a  fixed  point  as  origin ;  then  setting  out  as 
vertical  ordinates  the  amounts  you  have  calculated  for  the  cor- 
responding forces;    lastly,  connecting    by  a  curved   line  the 
system  of  points  thus  found. 

5.  Define  electrostatic  (or  electric)  "potential"  ;  and  calcu- 
late (by  the  rule  given  in  italics  in  Art.  263)  the  potential  at  a 
point  A,  which  is  at  one  corner  of  a  square  of  8  centimetres' 
side,  when  at  the  other  three  corners  B,  C,  D,  taken  in  order, 
charges  of  + 16,  +34,  and  +24  units  are  respectively  placed. 

Ans.  8  (very  nearly) , 


PROBLEMS   AND   EXERCISES  591 


6.  A  small  sphere  is  electrified  with  24  units  of  +  electricity. 
Calculate  the  potential  due  to  this  charge  at  points  1,  2,  3,  4,  5, 
6,  8,  and  10  centimetres'  distance  respectively.     Then  plot  out 
the  "  curve  of  potential  "  to  scale,  as  described  in  question  4. 

7.  A  small  sphere  charged  with   100  units  of  electricity  is 
dipped  into  a  hath  of  oil  having  a  dielectric  capacity  2 ;  find  the 
force  it  would  exert  on  a  unit  charge  5  centimetres  away. 

Ans.  2  dynes. 

8.  Distinguish  between  the   surface  density  at  a  point  and 
the  potential  at  that  point  due  to  neighbouring  charges. 

9.  What  are  equipotential  surfaces?     Why  is  the  surface 
of  an  insulated  conductor  an    equipotential    surface?      Is    it 
always  so  ? 

10.  Show  that  the  capacity  of  an  isolated  sphere  in  air  of 
radius  »'  has  a  capacity  eqiial  to  v  units.    What  is  the  electro-* 
static  unit  of  capacity  ? 

11.  Why  is  the  potential  of  the  earth  due  to  charges  that  we 
produce  practically  equal  to  zero? 

12.  A  sphere  whose  radius  is  14  centimetres  is  charged  until 
the  surface  density  has  a  value  of  10.    What  quantity  of  electri- 
city is  required  for  this?  Ans.  24,040  units  (nearly). 

13.  In  the  above  question  what  will  be  the  potential  at  the 
surface  of  the  sphere?   (See  Art.  269.)    Ans.  17GO  (very  nearly). 

14.  In  the  case  of  question  12,  what  will  be  the  electric  force 
at  a  point  outside  the  sphere  and  indefinitely  near  to  its  sur- 
face?    (Art.  276.)  Ans.  125'7  (very  nearly) . 

15.  Suppose  a  sphere  whose  radius  is  10  centimetres  to  be 
charged  with  6284  units  of  electricity,  and  that  it  is  then  caused 
i<>  share  its  charge  with  anon-electrified  sphere  whose  radius  is 
15  centimetres,  what  will  the  respective  charges  and  surface- 
densities  on  the  two  spheres  be  when  separated  ? 

Ans.  Small  sphere,  q  =2513*6,  ?=2: 
Large  sphere,  q  —  3770*4,  $  =  1*33. 

16.  A  charge  of  +  8  units  is  collected  at  a  point  20  centi- 
metres distant  from  the  centre  of  a  metallic  sphere  whose  radius 
is  10  centimetres.    It  induces  a  negative  electrification  at  the 
nearest  side  of  the  sphere.    Find  a  point  inside  the  sphere  such 
that  if  4  negative  units  were  placed  there  they  would  exercise  a 
potential  on  all  external  points  exactly  equal  to  that  of  the 
actual  negative  electrification.     (See  Art.  275.) 

Ans.  The  point  must  be  on  the  line  between  the  outside 
positive  charge  and  the  centre  of  the  sphere  and  at  5 
centims.  from  the  surface. 

17.  Two  large  parallel  metal  plates  are  charged  both  posi- 
tively but  unequally,  the  density  at  the  surface  of  A  being  +6, 


592  ELECTRICITY   AND   MAGNETISM 


that  at  the  surface  of  B  being  +  3.  They  are  placed  2  centi- 
metres apart.  Find  the  force  with  which  a  +  unit  of  electricity 
is  urged  from  A  towards  B.  Find  also  the  work  done  by  a  + 
unit  of  electricity  in  passing  from  A  to  B. 

Ans.  Electric  force  from  A  towards  B  =  18'85  dynes  ;  work 
done  by  unit  in  passing  from  A  to  B  =  37'5  ergs. 

18.  What  is  meant  by  the  dimensions  of  a  physical  quantity? 
Deduce  from  the   Law  of  Inverse   Squares  the  dimensions  of 
electricity;   and  show  by  this  means  that  electricity  is  not  a 
quantity  of  the  same  physical  dimensions  as  either  matter, 
energy,  or  force. 

19.  Explain  the  construction  and  principles  of  action  of  the 
quadrant  electrometer.    How  could  this  instrument  be  made 
self-recording? 

»  20.  Describe  the  construction  of  an  electrostatic  voltmeter, 
and  state  some  of  the  advantages  that  this  instrument  pos- 


21.  One  of  the  two  coatings  of  a  condenser  is  put  to  earth, 
to  the  other  coating  a  charge  of  5400  units  is  imparted.    It  is 
found  that  the  difference  of  potential  thereby  produced  between 
the  coatings  is  15  (electrostatic)  units.     What  was  the  capacity 
of  the  condenser  ?  Ans.  360. 

22.  What  is  the  meaning  of  specific,  inductive,  capacity? 
AVhy  does  hot  glass  appear  to  have  a  higher  specific  inductive 
capacity  than  cold  glass  ? 

23.  Describe  a  method  of  mapping  out  the  lines  of  force  in 
an  electrostatic  field. 

24.  Two  condensers  of  capacity  4  and  6  respectively  are 
placed  in  parallel;   and  in  series  with  them  is  placed  another 
condenser    having    a    capacity  of    5    microfarads.      Find    the 
capacity  of  the  whole  combination.  Ans.  3'3. 

25.  Compare  the  phenomenon  of  the  residual  charge  in  a 
Leyden  jar  with  the  phenomenon  of  polarization  in  an  electro- 
lytic cell. 

2(5.  A  condenser  was  made  of  two  flat  square  metal  plates, 
the  side  of  each  of  them  being  35  centimetres.  A  sheet  of 
indiarubber  -4  centim.  thick  was  placed  between  them  as  a 
dielectric.  The  specific  inductive  capacity  of  indiarubber  being 
taken  as  2'25,  calculate  the  capacity  of  the  condenser. 

Ans.  548'8  electrostatic  units. 

27.  Calculate  (in  electrostatic  units)  the  capacity  of  a  mile 
of  telegraph  cable,  the  core  being  a  copper  wire  of  '18  centim. 
diameter,  surrounded  by  a  sheathing  of  guttapercha  -91  centim. 
thick.  \k  for  guttapejcha  =  2'46 ;  one  mile  =  160,933  centims.] 

Ans.  82,164  units. 


PROBLEMS   AND   EXERCISES  593 


28.  A  Leyden  jar  is  made  to  share  its  charge  with  two  other 
jars,  each  of  which  is  equal  to  it  in  capacity.      Compare  the 
energy  of  the  charge  in  one  jar  with  the  energy  of  the  original 
charge.  Ans.  One  ninth  as  great. 

29.  A  series  of  Leyden  jars  of  equal  capacity  are  charged 
"in  cascade."     Compare  the  total  energy  of  the  charge  of  the 
individual  jars  thus  charged,  with  that  of  a  single  jar  charged 
from  the  same  source. 

30.  Classify  the  various  modes  of  discharge,  and  state  the 
conditions  under  which  they  occur. 

31.  Suppose  a  condenser,  whose  capacity  is  10,000  charged 
to  potential  14,  to  be  partially  discharged  so  that  the  potential 
fell  to  5.      Calculate  the  amount    of    heat  produced    by  the 
discharge,  on  the  supposition  that  all  the  energy  of  the  spark 
is  converted  into  heat.  Ans    '020357  of  a  unit  of  heat. 

32.  How  do  changes  of  pressure  affect  the  passage  of  electric 
sparks  through  air  ? 

33.  Describe  some  of  the  properties  of  matter  in  its  ultra- 
gaseous  or  radiant  state. 

34.  Why  are  telegraphic  signals  through  a  submerged  cable 
retarded    in  transmission,   and    how  can  this    retardation  be 
obviated  ? 

35.  How  is  the  difference  of  potential  between  the  earth  and 
the  air  above  it  measured?  and  what  light  do  such  measure- 
ments throw  on  the  periodic  variations  in  the  electrical  state  of 
the  atmosphere  ? 

36.  What  explanation  can  be  given  of  the  phenomenon  of 
a  thunderstorm  ? 

37.  What  are  the  essential   features  which  a  lightning-con- 
ductor must  possess  before  it  can  be  pronounced  satisfactory  ? 
And  what  are  the  reasons  for  insisting  on  these  points  ? 

38.  How  can  the  duration  of  an  electric  spark  be  measured  ? 


QUESTIONS  ON  CHAPTER  V 

1.  Define  magnetic  potential,  and  find  the  (magnetic)  potential 
due  to  a  bar  magnet  10  centimetres  long,  and  of  strength  80,  at 
a  point  lying  in  a  line  with  the  magnet  poles  and  6  centimetres 
distant  from  its  N-seeking  end.  Ans.  8'3. 

2.  A  N-seeking  pole  and  a  S-seeking  pole,  whose  strengths 
are  respectively  +  120  and  —  HO,  are  in  a  plane  at  a  distance  of 
6  centimetres  apart.      Find  the  point  between  them  where  the 
potential  is  =  0 ;  and  through  this  point  draw  the  curve  of  zero 
potential  in  the  plane. 

2Q 


504  ELECTRICITY   AND   MAGNETISM 


3.  Define   "intensity  of    the    magnetic  field."      A  magnet 
whose  strength  is  270  is  placed  in  a  uniform  magnetic  field 
whose  intensity  is  '166.    What  are  the  forces  which  act  upon  its 
poles?  Ans.  +  45  dynes  and  —  45  dynes. 

4.  Define    "intensity    of    magnetization."      A    rectangular 
bar-magnet,  whose  length  was  9  centimetres,  was  magnetized 
until  the  strength  of  its  poles  was  164.    It  was  2  centimetres 
broad  and  '5  centimetre  thick.     Supposing  it  to  be  uniformly 
magnetized  throughout  its  length,  what  is  the  intensity  of  the 
magnetization?  Ans.  164. 

5.  A  certain  electric  motor  has  100  conductors  on  its  arma- 
ture, each  carrying  10  amperes.      The  number  of  lines  of  force 
passing  through  the  armature  is  500,000.      Find  the  work  (in 
ergs)  done  in  one  revolution  of  the  armature. 

As  each  conductor  cuts  the  lines  twice  in  one  revolution  the 
answer  will  be  100,000,000  ergs. 

6.  Find  the  torque  (see  Art.  136)  on  the  armature  described 
in  the  last  question.    Note  that  with  the  above  data  the  torque 
is  independent  of  the  radius  of  the  armature,  for  the  force  on 
each  conductor  is  proportional  to  the  strength  of  the  field,  and 
this  is  inversely  proportional  to  the  radius  if  N  remains  the 

same'  Ans.  mmm  dyne-centimetres. 

I.  A  current  whose  strength  in  "  absolute  "  electromagnetic 
units  was  equal  to  0'05  traversed  a  wire  ring  of  2  centimetres 
radius.    What  was  the  strength  of  field  at  the  centre  of  the 
ring?    What  was  the  potential  at  a  point  P  opposite  the  middle 
of  the  ring  and  4  centimetres  distant  from  the  circumference  of 
the  ring?  Ans.f=  '1571 ;  V  =  ±  0-0421. 

8.  (a)  A  spiral  of  wire  of  1000  turns  carries  a  current  of  1 
ampere.    Find  the  total  magnetomotive  force  which  it  exerts. 

Ans.  1257. 

(b)  If  the  spiral  were  1  metre  in  length  and  1  centimetre  in 
diameter,  find  the  force  on  a  unit  pole  placed  (1)  in  its  centre ; 
(2)  at  its  end.  Ans.  12'57  dynes  and  6'28  dynes. 

9.  What  limits  are  there  to  the  power  of  an  electromagnet  ? 

10.  What  is  the  advantage  in  using  an  iron  core  in  an  electro- 
magnet ? 

II.  A  rod  of  soft  iron,  0'32  cm.  in  diameter  and  1  metre  long 
is  uniformly  overwound  from  end   to  end  with  an  insulated 
copper  wire  making  637  turns  in  one  layer.      Find  (using  Bid- 
well's  data  in  Art.  365)  what  strength  of  poles  this  rod  will 
acquire  when  a  current  of  5  amperes  is  sent  through  the  coil. 

Ans.  98'9  units. 


PROBLEMS   AND   EXERCISES  595 


12.  Enunciate  Maxwell's  rule  concerning  magnetic  shells, 
and  from  it  deduce  the  laws  of  parallel  and  oblique  currents 
discovered  by  Ampere. 

13.  A  circular  copper  dish  is  joined  to  the  zinc  pole  of  a 
small  battery.      Acidulated  water  is    then    poured    into  the 
dish,  and  a  wire  from  the  carbon  pole  of  the  battery  dips  into 
the  liquid  at  the  middle.      A  few  scraps  of  cork  are  thrown 
in  to  render  any  movement  of  the  liquid  visible.      What  will 
occur  when  the  N-seeking  pole  of  a  strong  bar-magnet  is  held 
above  the  dish  ? 

14.  Roget  hung  up  a  spiral  of  copper  wire  so  that  the  lower 
end  just  dipped  into  a  cup  of  mercury.    When  a  strong  current 
was  sent  through  the  spiral  it  started  a  continuous  dance,  the 
lower  end  producing  bright  sparks  as  it  dipped  in  and  out  of 
the  mercury.    Explain  this  experiment. 

15.  It  is  believed,  though  it  has  not  yet  been  proved,  that 
ozone  is  more  strongly  magnetic  than  oxygen.     How  could  this 
be  put  to  proof  ? 

16.  What  is  meant   by  the  permeability  of   a  substance? 
State  some  substances  in  which  it  is  constant,  and  some  in 
which  it  varies. 

17.  Describe  a  method  of  measuring  the   permeability  of 
iron. 

18.  A  ring  of  iron  is  wound  with  two  coils.      One  coil  is 
connected  to  a  ballistic  galvanometer,  and  on  connecting  the 
other  to  a  battery  a  throw  of  the  needle  of  160  scale  divisions 
is  observed.    The  current  is  then  broken  and  there  is  a  throw 
of  40  divisions  in  the  opposite  direction.    Why  are   the    two 
throws  not  equal  ?    What  change  has  taken  place  in  the  iron  ? 
How  would  you  bring  it  back  to  its  original  condition  ? 

19.  Sketch  a  closed    hysteresis   curve  for  hard    steel,   for 
which,  when  H  is  raised  to  100,  B  =  12,800,  and  for  which  the 
remanence  is  9500  and  the  coercive  force  40. 

20.  An  iron  bar  30  centimetres  long  and  10  square  centi- 
metres in  sectional  area  is  bent  into  the  shape  of  a  horse-shoe 
for  the  purpose  of  making  an  electromagnet  which  shall  have 
a  pull  of  66  kilograms  upon  its  armature  (a  bar  12  centimetres 
long  and  10  square  centimetres  in  section)  when  it  is  5  inch 
away  from    its    poles.     Find   the    number    of    ampere    turns 
required,  assuming  a  leakage  of  one-third  of  the  lines  of  force. 

Taking  the  formula :  — 

^  X  20  sq.  cms.  of  pole  face  =  66,000  X  981  dynes, 

OTT 

we  get  B  =  9000.    From  the  table,  Art.  364,  ^  for  the  armature 


596  ELECTRICITY   AND   MAGNETISM 


=  2250,  B  for    the    horse  -  shoe  =  1  '5  x  9000=  13,500,   so   that 
^2  =  900,  then  ampere-turns  = 


21.  What  thickness  of  copper  wire  must  be  used  to  wind  the 
above  magnet  in  order  to  obtain  18,930  ampere  turns,  the  wind- 
ing on  each  cylindrical  bobbin  having  a  mean  diameter  of  7 
centimetres,  if  the  pressure  at  the  terminals  of  the  magnet  is 
intended  to  be  100  volts  ? 

If  r  is  the  resistance  of  one  turn,  and  5  the  number  of  turns, 

r  =  E.  =     10°    •  but  we  know  that  r  =   7  X  w   x  1-6  X  10-6. 

CS         18,930  d2X  ITT 


Hence  diameter    of    wire,   d  =     /-*  =  0.Q92 

\ 


,  X  7  X  4  X  TC 

cms.  \  106x100 


N.B.  —  The  thickness  of  wire  is  independent  of  the  number 
of  turns  (except  in  so  far  as  this  affects  the  mean  diameter  of 
the  bobbin)  ,  but  the  greater  the  number  of  turns  the  less  will  be 
the  number  of  watts  expended. 

22.  What  is  the  object  of  "polarizing"  the  armature  of  a 
magnet  in  a  piece  of  mechanism,  such  as  a  relay? 

23.  Describe  the  construction  of  a  current-balance,  and  the 
mode  of  using  it. 

QUESTIONS  ON  CHAPTER  VI 

1.  The  resistance  of  telegraph  wire  being  taken  as  13  ohms 
per  mile,  and  the  E.M.F.  of  a  Leclanche  cell  as  I'  4:  volt,  calculate 
how  many  cells  are  needed  to  send  a  current  of  12  milli-amperes 
through  a  line  120  miles  long;  assuming  that  the  instruments  in 
circuit  offer  as  much  resistance  as  20  miles  of  wire  would  do, 
and  that  the  return  current  through  earth  meets  with  no  appre- 
ciable resistance.  Ans.  1(5  cells. 

2.  Fifty  Grove's  cells  (E.M.F.  of  a  Grove  =  1'8  volt)  are  united 
in  series,  and  the  circuit  is  completed  by  a  wire  whose  resistance 
is  15  ohms.    Supposing  the  internal  resistance  of  each  cell  to  be 
0'3  ohm,  calculate  the  strength  of  the  current. 

Ans.  3  amperes. 

3.  The  current  running  through  an  incandescent  filament  of 
carbon  in  a  lamp  was  found  to  be  exactly  1  ampere.    The  differ- 
ence of  potential  between  the  two  terminals  of  the  lamp  while 
the  current  was  flowing  was  found  to  be  30  volts.    What  was 
the  resistance  of  the  filament  ? 

4.  Define  specific  resistance.    Taking  a  specific  resistance  of 
copper  as  1642,  calculate  the  resistance  of  a  kilometre  of  copper 
wire  whose  diameter  is  1  millimetre.  Ans.  20'9  ohms. 


PROBLEMS  AND  EXERCISES  597 


5.  On  measuring  the  resistance  of  a  piece  of  No.  30  B.  W.  G. 
(covered)  copper  wire,  18'12  yards  long,  I  found  it  to  have  a 
resistance  of  3'02  ohms.    Another  coil  of  the  same  wire  had  a 
resistance  of  22'6'5  ohms ;  what  length  of  wire  was  there  in  the 
coil?  Ans.  135-9  yards. 

6.  Calculate  the  resistance  of  a  copper  conductor  one  square 
centimetre  in  area  of  cross-section,  and  long  enough  to  reach 
from   Niagara  to  New  York,  reckoning  this  distance  as  480 
kilometres.  Ans.  78'8  ohms. 

7.  Find  the  drop  in  volts  if  400  amperes  is  passed  through 
this  conductor.     What  would  be  the  waste  of  power  (in  ivatts)  ? 

Ans.  31,520  volts,  12,608,000  watts. 

<S.  The  resistance  from  plate  to  plate  in  a  certain  electrolytic 
bath  is  0*9  of  an  ohm.  You  wish  to  pass  through  it  the 
strongest  current  you  can  get  from  20  Daniell  cells,  each  with 
a  resistance  of  one  ohm.  How  would  you  group  the  cells? 

Ans.  4  in  series,  5  rows  in  parallel. 

9.  The  specific;  resistance  of  guttapercha  being  3'5  X  1023, 
calculate  the  number  of  coulombs  of  electricity  that  would 
leak  in  one  century  through  a  sheet  of  guttapercha  one  centi- 
metre thick  and  one  metre  square,  whose  faces  were  covered 
with  tinfoil  and  joined  respectively  to  the  poles  of  a  battery  of 
100  Darnell's  cells.  Ans.  9'7  coulombs. 

10.  Six  Daniell's  cells,  for  each  of  which  E  —  1-05  volt,  r  = 
0'5  ohm,  are  joined  in  series.     Three  wires,  X,  Y,  and  Z,  whose 
resistances  are  severally  3,  30,  and  300  ohms,  can  be  inserted 
between  the  poles  of  the  battery.    Determine  the  current  which 
flows  when  each  wire  is  inserted  separately;   also  determine 
that  which  flows  when  they  are  all  inserted  at  once  in  parallel. 

Ans.  Through  X  T05     amperes. 

Through  Y  0'1909 

Through  Z  0'0207 

Through  all  three  T105          " 

11.  Calculate  the  number  of  cells  required  to  produce  a  cur- 
rent of  50  milli-amperes  through  a  line  114  miles  long,  whose 
resistance  is  12$  ohms  per  mile,  the  available  cells  of  the  bat- 
tery having  each   an  internal  resistance  of  1*5  ohm,  and  an 
E.M.F.  of  1-5  volt.  Ans.  50  cells. 

12.  You  have  20  large  Leclanche  cells  (E.M.F.  =  T5  volt,  r  = 
0'5  ohm  each)  in  a  circuit  in  which  the  external  resistance  is  10 
ohms.    Find  the  strength  of  current  which  flows  (a)  when  the 
cells  are  joined  in  simple  series;  (b)  all  the  zincs  are  united, 
and  all  the  carbons  united,  in  parallel  arc;  (c)  when  the  cells 
are  arranged  two  abreast  (i.e.  in  two  files  of  ten  cells  each) ; 
(d)  when  the  cells  are  arranged  four  abreast. 

Ans.  (a)  1-5;  (6)  0'149G;  (c)  1-2;  (d)  0'702  ampere. 


598  ELECTRICITY  AND   MAGNETISM 


13.  With  the  same  battery  how  would  you  arrange  the  cells 
in  order  to  telegraph  through  a  line  100  miles  long,  reckoning 
the  line  resistance  as  12£  ohms  per  mile  ? 

14.  Show  that,  if  we  have  a  battery  of  n  given  cells  each  of 
resistance  r  in  a  circuit  where  the  external  resistance  is  R,  the 
strength  of  the  current  will  be  a  maximum  when  the  cells  are 
coupled  up  in  a  certain  number  of  rows  equal  numerically  to 

\/nr  -f-  R. 

15.  Two  wires,  whose  separate  resistances  are  28  and  24, 
are  placed  in  parallel  in  a  circuit  so  that  the  current  divides, 
part  passing  through  one,   part   through   the  other.      What 
resistance  do  they  offer  thus  to  the  current  ? 

Ans.  12-92  ohms. 

16.  Using  a  large  bichromate  cell  of  practically  no  internal 
resistance,  a  deflexion  of  9°  was  obtained  upon  a  tangent  gal- 
vanometer (also  of   small  resistance)  through  a  wire  whose 
resistance  was  known  to  be  435  ohms.      The  same  cell  gave  a 
deflexion  of  5°  upon  the  same  galvanometer  when  a  wire  of 
unknown  resistance  was  substituted  in  the  circuit.      What  was 
the  unknown  resistance  ?  Ans.  790  ohms. 

17.  In  a  Wheatstone's  bridge,  in  which  resistances  of  10  and 
100  ohms  respectively  were  used  as  the  fixed  resistances,  a  wire 
whose  resistance  was  to  be  determined  was  placed :  its  resist- 
ance was  balanced  when  the  adjustable  coils  were  arranged  to 
throw  281  ohms  into  circuit.    What  was  its  resistance  ? 

Ans.  28-1  ohms. 

18.  Describe  the  method  of  using  a  metre  bridge  to  measure 
resistances. 

19.  Give  the  proof  of  Foster's  method  of  measuring  small 
differences  of  resistance  from  the  consideration  of  Ohm's  law. 

20.  To  find  the  voltage  of  a  dynamo  you  connect  to  its 
brushes  the  ends  of  a  German-silver  wire  120  feet  long,  wound 
on  an  insulating  cylinder,  and  find  that  when  one  terminal  of 
a  Daniell  cell  (1*05  volt)  is  joined  to  a  point  on  the  wire,  and 
the  other  terminal  in  series  with  a  galvanometer  is  connected 
to  another  point  1  ft.  from  the  first,  no  deflexion  is  observed. 
What  is  the  voltage  of  the  dynamo  ?  Ans.  126  volts. 

21.  A  battery  of  5  Leclanche  cells  was  connected  in  simple 
circuit  with  a  galvanometer  and  a  box  of  resistance  coils.     A 
deflexion  of  39°  having  been  obtained  by  adjustment  of  the 
resistances,  it  was  found  that  the  introduction  of  150  addi- 
tional ohms  of  resistance  brought  down  the  deflexion  to  22°. 
Assuming  the  galvanometer  to  have  140  ohms  resistance,  find 
the  internal  resistance  of  the  battery.  Ans.  10  ohms. 

22.  How  are  standard  resistance  coils  wound,   and  why? 
What  materials  are  they  made  of,  and  why  ? 


PROBLEMS   AND   EXERCISES  599 


23.  Three  very  small  Dani ell's  cells  gave,  with  a  sine  gal- 
vanometer (itself  of  no  appreciable  resistance),  a  reading  of 
57°.    On  throwing  20  ohms  into  the  circuit  the  galvanometer 
reading  fell  to  25J.    Calculate  the  internal  resistance  of  the 
cells.  Ans.  6'6  ohms  each. 

24.  A  length  of  telegraph  cable  was  plunged  in  a  tub  of 
water  and  then  charged  for  a  minute  from  a  battery  of  120 
Darnell's  cells.    The  cable  was  then  discharged  through  a  long- 
coil  galvanometer  with 'a  needle  of  slow  swing.    The  first  swing 
was  40°.  A  condenser  whose  capacity  was  3  microfarad  was  then 
similarly  chai-ged  and  discharged ;  but  this  time  the  first  swing 
of  the  needle  was  only  14°.     What  was  the  capacity  of  the  piece 
of  cable?  Ans.  0'934 microfarad. 

25.  Using  an  absolute  electrometer,  Lord  Kelvin  found  the 
difference  of  potential  between  the  poles  of  a  Daniell's  cell  to 
be  0-00374  electrostatic  units  (C.G.S.  system).    The  ratio  of  the 
electrostatic  to  the  electromagnetic  unit  of  potential  is  given 
in  Art.  359,  being  =  1/v.    The  volt  is  defined  as  108  electromag- 
netic units.    From  these  data  calculate  the  E.M.F.  of  a  Daniell's 
cell  in  volts.  Ans.  1-115  volt. 

26.  The  radius  of  the  earth  is  approximately  03  X  IQ7  centi- 
metres.    The  ratio  of  the  electrostatic  to  the  electromagnetic 
unit  of  capacity  is  given  in  Art.  359.     The  definition  of  the 
farad  is  given  in  Art.  354.      Calculate  the  capacity  of  the 
earth  (regarded  as  a  sphere)  in  microfarads. 

Ans.  700  microfarads  (nearly). 

27.  The  electromotive-force  of  a  Daniell's  cell  was  deter- 
mined by  the  following  process :  —  Five  newly-prepared  cells 
were  set  up  in    series  with  a  tangent    galvanometer,  whose 
constants  were  found  by  measurement.    The  resistances  of  the 
circuit  were  also  measured,  and  found  to  be  in  total  16'9  ohms. 
Knowing  the  resistance  and  the   absolute   strength  of  current 
the  E.M.F.  could  be  calculated.    The  deflexion  obtained  was 
45°,  the  number  of  turns  of  wire  in  the  coil  10,  the  average 
radius  of  the  coils  11  centimetres,  and  the  value  of  the  hori- 
zontal component  of  the  earth's  magnetism  at  the  place  was 
0-18  G.C.S.  units.    Deduce  the  E.M.F.  of  a  Daniell's  cell. 

Ans.  1-OG47  X  108  G.C.S.  units,  or  1*0647  volt. 

28.  Apply  the  formula  of  the  ballistic  galvanometer  (Art. 
418,  6)  to  determine  the  number  of  magnetic  lines  cut  by  an 
exploring  coil  (Art.  366,  b)  when  the  magnetism   in  the  core 
on  which  it  is  wound  is  suddenly  reversed.     If  R  is  the  resist- 
ance of  the  circuit,  Q  =  2N/R.     Hence  the  answer  is  N  =  RT 
sin  i 0/2*8,  where  S  is  the  number  of  turns  in  the  exploring 
coil. 

29.  Suppose  a  copper  disk  to  revolve  in  a  field  produced  by 
a  fixed  coil  closely  surrounding  its  circumference.     In  circuit 
with  the  coil  is  a  small  battery  and  a  resistance  wire.     In  the 


600  ELECTRICITY  AND   MAGNETISM 


wire  are  found  two  points  such  that  the  fall  of  potential  between 
them  is  equal  to  the  volts  generated  between  the  centre  and 
circumference  of  the  revolving  disk.  By  balancing  these  with 
a  galvanometer  Lorenz  was  able  to  calculate  in  absolute  meas- 
ure the  resistance  of  the  wire.  If  M  be  the  coefficient  of  mutual 
induction  between  the  circumference  of  the  disk  and  the  sur- 
rounding coil,  and  T  the  period  of  revolution  of  the  disk,  show 
that  R  the  resistance  between  the  points  =  M-r  T. 

Ans.  Since  N  the  magnetic  flux  through  the  disk  =  MC, 
and  E  =  N/T,  and  C  =  E/R,  it  follows  that  CR  = 
MC/T,  whence  R  =  M/T.  Q.E.D. 


QUESTIONS  ON  CHAPTER  VII 

1.  A   strong  battery-current   is  sent,   for  a  few  moments, 
through  a  bar  made  of  a  piece  of  antimony  soldered  to  a  piece 
of  bismuth.    The  battery  is  then  disconnected  from  the  wires 
and   they  are  joined  to  a  galvanometer  which  shows  a  de- 
flexion.   Explain  this  phenomenon. 

2.  A  long  strip  of  zinc  is  connected  to  a  galvanometer  by 
iron  wires.    One  junction  is  kept  in  ice,  the  other  is  plunged 
into  water  of  a  temperature  of  50°  C.    Calculate,  from  the  table 
given  in  Art.  422,  the  electromotive-force  which  is  producing 
the  current.  Ans.  690  microvolts. 

3.  When  heat  is  evolved  at  a  junction  of  two  metals  by  the 
passage  of  a  current,  how  would  you  distinguish  between  the 
heat  due  to  resistance  and  the  heat  due  to  the  Peltier  effect  ? 

4.  Lord  Kelvin  discovered  that  when  a  current  flows  through 
iron  it  absorbs  heat  when  it  flows  from  a  hot  point  to  a  cold 
point ;  but  that  when  a  current  is  flowing  through  copper  it 
absorbs  heat  when  it  flows  from  a  cold  point  to  a  hot  point. 
From  these  two  facts,  and  from  the  general  law  that  energy 
tends  to  run  down  to  a  minimum,  deduce  which  way  a  current 
will  flow  round  a  circuit  made  of  two  half-rings  of  iron  and 
copper,  one  junction  of  which  is  heated  in  hot  water  and  the 
other  cooled  in  ice. 

5.  Give  a  curve  showing  the  increase  and  decrease  of  the 
thermo-electromotive-force  as  a  junction  of  iron  and  copper  is 
raised  from  0°  C.  to  400°  C.,  and  explain  it  by  means  of  the 
thermo-electric  diagram  of  Professor  Tait. 


QUESTIONS  ON  CHAPTER  VIII 

1.  Calculate  by  Joule's  law  the  number  of  calories  developed 
in  a  wire  whose  resistance  is  4  ohms  when  a  steady  current  of 
0'14  ampere  is  passed  through  it  for  ten  minutes. 

Ans.  11'2  calories. 


PROBLEMS  AND   EXERCISES  601 


2.  Why  does  the  platinum   wire  in  a  Cardew   voltmeter, 
when  a  steady  voltage  is  applied  to  it,  rise  to  a  certain  tem- 
perature and  then  remain  at  that  temperature  without  altera- 
tion? 

3.  Show  from  the  definitions  of  the  horse-power  and  of  the 
watt,  and  from  the  relations  between  the  pound  and  the  gramme, 
the  foot  and  the  centimetre,  that  there  are  74(5  watts   in  one 
horse-power. 

4.  Explain  why  you  would   expect  the  heat  produced  in  a 
conductor  to  be  proportional  to  the  square  of  the  current. 

5.  Describe  the  construction  of  a  watt   meter   and  explain 
how  you  would  connect  it  up  to  measure  the  power  supplied  to 
an  electric  motor. 

6.  Explain  why  it    is  advantageous  to  distribute  electric 
energy  at  a  high  voltage.    There  is  already  laid  a  copper  main 
having  a  resistance  of  0'5  of  an  ohm  along  which  it  is  desired  to 
transmit  4  kilowatts,  and  to  deliver  it  at  the  far  end  at  a  pressure 
of  100  volts.    Which  would  be  the  more  efficient  method  of  the 
two  following,  to  send  40  amps,  at  an  initial  pressure  of  120  volts, 
or  to  send  a  current  at  a  pressure  of  2400  volts,  using  a  trans- 
former with  an  efficiency  of  85  per  cent? 

Ans.  The  latter  method  would,  have  an  efficiency  of  84-9 
per  cent,  the  former  of  83'3  per  cent. 

7.  Mention  some  of  the  principles  upon  which  supply  meters 
have  been  designed. 

8.  An  electric  motor  is  supplied  at  a  pressure  of  100  volts : 
the  armature  resistance  is  O'Ol  ohm.    When  it  is  supplying  20 
horse-power,  what  is  its  electrical  efficiency? 

-4ns.  98'5  per  cent. 

9.  Show  under  what  circumstances  an  electric  motor  is  most 
efficient. 

10.  Enumerate  the  principal  parts  of  an  arc  lamp. 

11.  Why  in  a  continuous-current  arc  lamp  is  the  current 
usually  sent  downwards  rather  than  upwards? 

12.  Why  does  the  filament  of  an  incandescent  lamp   get 
hotter  than  the  platinum  leading-in  wires  ? 

13.  Explain  by  a   diagram   the  system  of   three-wire  dis- 
tribution ;  and  point  out  its  advantage  over  a  two-wire  distri- 
bution. 

14.  A  current  of  9  amperes  worked  an  electric  arc  light,  and 
on  measuring  the  difference  of  potential  between  the  two  car- 
bons by  an  electrometer  it  was  found  to  be  50  volts.    What  was 
the  amount  of  horse-power  absorbed  in  this  lamp  ? 

-4ns.  0'603  horse-power. 


602  ELECTRICITY  AND   MAGNETISM 


QUESTIONS   ON  CHAPTER  IX 

1.  The  reluctance  of  the  core  of  a  certain  transformer  is 
0'002.    Find  the  coefficient  of  mutual  induction  between  the 
primary  and  secondary  coils  which  have  1000  and  50  turns 
respectively,  assuming  no  magnetic  leakage. 

Ans.  0-628  hem-y. 

2.  A  battery  current  is  sent  through  the  primary  of  this 
transformer.     State  from  Lenz's  law  the  direction  (relatively 
to  this  current)  of  the  E.M.F.'s  induced  in  both  the  primary 
and  secondary,  (a)  when  the  current  is  starting,  (b)  when  it  is 
ceasing. 

3.  Foucault  set  the  heavy  bronze  wheel  of  his  gyroscope 
spinning  between  the  poles  of  a  powerful  electromagnet,  and 
found  that  the  wheel  grew  hot.    What  was  the  cause  of  this? 
Where  did  the  heat  come  from  ? 

4.  You  try  to  turn  a  copper  disk  between  the  poles  of  a 
magnet.     If  you  move  it  slowly  it  goes  quite  easily,  if  you  try 
to  move  it  quickly  it  resists.    Why  is  this?    What  is  the  force 
required  to  turn  it  proportional  to? 

5.  The  shunt  coil  of  a  certain  dynamo  has  a  resistance  of 
40  ohms.     It  is  switched  on  to  a  battery  of  accumulators  yield- 
ing 100  volts,  and  one  second  afterwards  the  current  has  risen 
to  0'9825  of  an  ampere.     Find  the  coefficient  of  self-induction  of 
the  shunt  coil.    Assume  log  0'607  =  i"783  and  log  e  =  0'434. 

Ans.  80  henries. 

6.  If  a  battery  of  10  cells  each  of   1*4  volt  and  2  ohms 
resistance  be  applied  to  a  circuit  which  has  a  resistance  of  5 
ohms  and  inductance  O'l  henry,  find  what  modes  of  grouping 
the  cells  are  best  (a)  to  give  the  largest  steady  current,  (6)  to 
give  the  largest  current  at  the  end  of  losa  second,  (c)  to  give  the 
largest  amount  of  external  work  relatively  to  the  weight  of 
zinc  consumed. 

Ans.  (a)  5  in  series,  2  rows  in  parallel.    (6)  All  in  series, 
(c)  All  in  parallel. 


QUESTIONS  ON  CHAPTER  X 

1.  What  devices  are  employed  in  continuous  current  dy- 
namos to  obtain  (a)  a  current  continuously  in  one  direction, 
(6)  a  current  of  uniform  strength? 

2.  Apply    Fleming's    Rule   (Art.  226)    to    determine  which 
way  the  electromotive-forces  will  operate  in  a  ring  armature 


PROBLEMS  AND   EXERCISES  603 


(gramme)  wound  right-handedly  over  the  core  revolving  right- 
handedly  in  a  horizontal  magnetic  field  having  the  N  pole  on 
the  right  hand. 

Am.  The  induced  E.M.F.'s  tend  to  make  the  currents 
climb,  in  both  the  ascending  and  descending  halves, 
toward  the  highest  point  of  the  ring. 

3.  A  dynamo's  field  magnet  gives  a  flux  of  9,000,000  lines. 
How  many  conductors  must  there  be  on  the  armature  in  order 
that  the  dynamo  may  generate  108  volts  when  driven  at  a  speed 
of  600  revolutions  per  minute?  Ans.  120. 

4.  You  have  an  engine  which  will  drive  a  dynamo  at  a  fairly 
constant  speed  at  all  loads.    How  would  you  excite  the  dynamo 
if  it  were  intended  for  lighting  by  incandescent  lamps  ?     Make 
a  diagrammatic  sketch  of  all  necessary  connexions,  including 
the  lamp  circuit. 

5.  Take  the  equation  E  =  a  sin  (2irnt).      Let  a  =  140  and 
n  =  100.     Now  take  different  values  for  t,  beginning  t  =  "0005 
of  a  second,   then   t  =  '001,  taking  20  different  values  until 
t  —  "01.    Fill  in  the  values  in  the  above  equation  and  find  the 
corresponding  20  values  of  E.     Then  plot  on  squared  paper 
taking  E  as  ordinate  and  t  as  abscissae.    The  result  will  be  a 
curve  like  that  shown  in  Fig.  251. 

6.  Repeat  the  process  of  the  last  question,  taking  the  equa- 
tion G  =  b  sin  (2nnt  —  4>),  where  b  =  20,  n  =  100,  and  </>  =  0;5 
radian.    Plot  the  results  upon  the  same  paper  as  the  curve  in 
the  last  equation  was  plotted.    One  curve  represents  the  E.M.F. 
at  each  instant,  the  other  the  lagging  current. 

7.  An  alternating  pressure  of  100  (virtual)  volts  following 
a  sine  law  with  a  frequency  of  100  per  second  is  applied  to  the 
ends  of  a  coil  having  a  resistance  of  8  ohms  and  a  coefficient  of 
self-induction  of  O'OOS  henry ;  find  the  current  that  will  flow  and 
the  angle  of  lag. 

Ans.  Current  =  11'6  amperes ;  lag  =  22  degrees. 

8.  An   alternate-current   magnet   with    properly    laminated 
core  has  a  coil  of  160  turns,  and  a  coefficient  of  self-induction 
of  0'005  of  a  henry.    What  alternating  voltage  of  frequency 
100  per  second  must  be  applied  to  it  in  order  to  obtain  4800 
ampere-turns,  assuming  the  resistance  to  be  negligible? 

Ans.  47-1. 

9.  How  much  resistance  must  be  put  in  circuit  with  the  coils 
of  this  magnet  in  order  that  the  angle  of  lag  may  be  45°  ? 

Ans.  3-14. 

10.  An  alternate-current  transformer  is  designed  to  give  out 
40  amperes  at  a  pressure  of  50  volts  at  its  secondary  terminals. 
No.  of  windings  300  primary;   12  secondary.     Resistances  12 


604  ELECTRICITY   AND   MAGNETISM 


ohms,  primary;  0'014  ohm,  secondary.  Find  the  coefficient  of 
transformation,  and  the  volts  that  must  be  applied  at  the  pri- 
mary terminals. 

Ans.  Coefficient  of  transformation  is  25;  volts  at  pri- 
mary terminals  1283. 

11.  State  the  principles  upon  which  continuous-current  trans- 
formers are  made.    Why  is  it  necessary  to  have  a  moving  part 
in  continuous-current  transformers  and  not  in  alternate-current 
transformers  ? 

12.  Enumerate    three    distinct    kinds    of    alternate-current 
motors,  and  state  which  kind  is  synchronous  and  which  not. 

13.  An  alternate-current  synchronous  motor  is  supplied  from 
the  street  mains.    It  is  found  that  when  fully  loaded  it  takes 
more  current  than  when  lightly  loaded,  though  it  always  goes 
at  the  same  speed  and  the  volts  remain  constant.    Explain  how 
this  comes  about. 

14.  How  can  you  produce  a  rotatory  magnetic  field?     De- 
scribe some  of  its  properties. 

QUESTIONS  ON  CHAPTER  XI 

1.  It  is  found  that  a  single  Daniell's  cell  will  not  electrolyze 
acidulated  water,  however  big  it  may  be  made.     It  is  found,  on 
the   other  hand,  that  two  Daniell's  cells,  however  small,  will 
suffice  to  produce  continuous  electrolysis  of  acidulated  water. 
How  do  you  account  for  this  ? 

2.  From  the  table  of  electro-chemical  equivalents  (Art.  240) 
calculate  how  many  coulombs  it  will  take  to  deposit  one  grain 
of    the    following  metals: — Copper   (from    sulphate),   silver, 
nickel,  gold.  Ans.   Cu  3058,  Ag  891,  Ni  3280,  An  1473. 

3.  A  battery  of  2  Grove  cells  in  series  yields  a  current  of  5 
amperes  for  2  hours;  how  much  zinc  will  be  consumed,  assum- 
ing no  waste  ?  Ans.  24'2<>. 

4.  Calculate  the  E.M.F.  of  a  Daniell  cell  from  considerations 
of  the  heat  value  of  the  combinations  which  take  place  and  the 
quantity  of  the  elements  consumed,  taking  the  heat  value  for 
zinc  in  sulphuric  acid  as  1070  and  that  for  copper  as  90<)-5. 

Ans.  I'll  volts. 

5.  Describe  the    construction    and    working   of    a    modern 
secondary  battery. 

G.  Most  liquids  which  conduct  electricity  are  decomposed 
(except  the  melted  metals)  in  the  act  of  conducting.  How  do 
you  account  for  the  fact  observed  by  Faraday  that  the  amount 
of  matter  transferred  through  the  liquid  and  deposited  on  the 
electrodes  is  proportional  to  the  amount  of  electricity  trans- 
ferred through  the  liquid  ? 


PROBLEMS   AND   EXERCISES  605 


7.  Describe  the  process  for  multiplying  by  electricity  copies 
of  engravings  on  wood-blocks. 

8.  How  would  you  make  arrangements  for  silvering  spoons 
of  nickel-bronze  by  electro-deposition  ? 


QUESTIONS  ON  CHAPTER   XII 

1.  Sketch  an  arrangement  by  which   a  single  line  of  wire 
can  be  used  by  an  operator  at  either  end  to  signal  to  the 
other ;  the  condition  of  working  being  that  whenever  you  are 
not  sending  a  message  yourself  your  instrument  shall  be  in 
circuit  with  the  line  wire,  and  out  of  circuit  with  the  battery  at 
your  own  end. 

2.  What  advantages  has  the  Morse   instrument    over   the 
needle  instruments  introduced   into  telegraphy  by  Cooke  and 
Wheatstone  ? 

3.  Explain  the  use  and  construction  of  a  relay. 

4.  Show,  from  the  law  of  traction  (Art.  384),  that  the  change 
of  attracting  force  resulting  from  a  change  in  the  number  of 
magnetic  lines  that  enter  an  armature  will  be  greater  if  the 
system  is  polarized  (i.e.  magnetized  to  begin  with)  than  if  it  is 
non-polarized. 

Ans.  Since  /aN2,  it  follows  that  f  +  df  will  be  propor- 
tional to  (N  +  dN)2.  Expanding,  and  subtracting 
the  former,  and  neglecting  the  small  term  (dN)2,  we 
find  d/a  2N  •  dN ;  which  shows  that,  for  a  given  dN, 
d/ocN. 

5.  It  is  desirable  in  certain  cases  (duplex  and  quadruplex 
signalling)  to  arrange  telegraphic  instruments  so  that  they  will 
respond  only  to  currents  which  come  in  one  direction  through 
the  line.    How  can  this  be  done? 

6.  It  is  wished  to  make  a  sort  of  duplex  telegraph  by  using 
one  set  of  instruments  that  work  with  continuous  currents, 
the  other  set  with  rapidly  alternating  currents,  at  the  same 
time  on  the  same  line.    To  carry  out  this  idea  there  must  be 
found   (a)  an  apparatus  which   will   let   continuous  currents 
flow  through  it,  but  will  choke  off  alternate  currents;   (b)  an 
apparatus  which  will  transmit  alternate  currents,  but  cut  off 
continuous  currents.    What  apparatus  will  do  these  things? 

7.  A  battery  is   set   up  at  one   station.      A  galvanometer 
needle  at   a  station   eighty  miles  away  is  deflected  through  a 
certain   number  of  degrees  when   the  wire  of   its  coil  makes 
twelve  turns  round  the  needle ;  wire  of  the  same  quality  being 
used  for  both  line  and  galvanometer.    At  200  miles  the  same 
deflexion  is  obtained  when  twenty-four  turns  are  used  in  the 
galvanometer-coil.      Show  by  calculation  (a)  that  the  internal 


606  ELECTRICITY   AND   MAGNETISM 


resistance  of  the  battery  is  equal  to  that  of  40  miles  of  the 
line-wire;  (6)  that  to  produce  an  equal  deflexion  at  a  station 
360  miles  distant  the  number  of  turns  of  wire  in  the  galvan- 
ometer-coil must  be  40. 

8.  Suppose  an  Atlantic  cable  to  snap  off  short  during  the 

grocess  of  laying.      How  can  the  distance  of  the  broken  end 
rom  the  shore  end  be  ascertained  ? 

9.  Suppose  the  copper  core  of  a  submarine  cable  to  part  at 
some  point  in  the  middle  without  any  damage  being  done  to  the 
outer  sheath  of  guttapercha.     How  could  the  position  of  the 
fault  be  ascertained  by  tests  made  at  the  shore  end  ? 

10.  Explain  the  construction  and  action  of  an  electric  bell. 

11.  Describe  and  explain  how  electric  currents  are  applied 
in  the  instruments  by  which  very  short  intervals  of  time  are 
measured. 


QUESTIONS  ON  CHAPTER  XIII 

1.  Explain    the    use    of    Graham    Bell's    telephone   (1)    to 
transmit  vibrations ;  (2)  to  reproduce  vibrations. 

2.  Describe  a  form  of  telephone  in  which  the  vibrations  of 
sound  are  transmitted  by  means  of  the  changes  they  produce 
in  the  resistance  of  a   circuit  in   which  there  is  a  constant 
electromotive-force . 

3.  Two  coils,  A  and  B,  of  fine  insulated  wire,  made  exactly 
alike,  and  of  the  same  number  of  windings  in  each,  are  placed 
upon  a  common  axis,  but  at  a  distance  of  10  inches  apart. 
They  are  placed  in  circuit  with  one  another  and  with  the  second- 
ary wire  of  a  small  induction-coil  of  Ruhmkorff's  pattern,  the 
connexions  being   so  arranged    that   the  currents   run  round 
the  two  coils  in  opposite  directions.     A  third  coil  of  fine  wire, 
C,  has  its  two  ends  connected  with  a  Bell's  telephone,  to  which 
the  experimenter  listens  while  he  places  this  third  coil  between 
the  other  two.    He  finds  that  when   C  is  exactly  midway  be- 
tween A  and  B  no  sound  is  audible  in  the  telephone,  though 
sounds  are  heard  if  C  is  nearer  to  either  A  or  B.    Explain 
the  cause  of  this.    He  also  finds  that  if  a  bit  of  iron  wire  is 
placed  in  A  silence  is  not  obtained  in  the  telephone  until  C 
is  moved  to  a  position   nearer  to  B  than  the  middle.    Why 
is  this?    Lastly,  he  finds  that  if  a  disk  of   brass,  copper,  or 
lead  is  interposed  between  A  and  C,  the  position  of  silence 
for  C  is  now  nearer  to  A   than    the    middle.      How  is  this 
explained  ? 


PROBLEMS  AND   EXERCISES  607 


QUESTIONS  ON  CHAPTER  XIV 

1.  What  apparatus  would  you  use  to  produce  electric  oscilla- 
tions ?    Show  how  you  would  operate  it,  and  explain  why  the 
oscillations  take  place. 

2.  Explain  how  electric  oscillations  in  a  condenser  circuit 
produce  electric  waves  in  the  surrounding  medium. 

3.  The  capacity  of  an  air-condenser  is  O'OOl  of  a  microfarad. 
It  is  charged  and  then  discharged  through  a  circuit  having  a 
self-induction  of  0'004  of  a  henry  and  a  resistance  of  4  ohms. 
Find  the  frequency  of  the  vibration.  Ans.  n  =  159,100. 

4.  Under  what  circumstances  do  oscillations  not  take  place 
when  a  condenser  is  discharged  ? 

5.  If  the  frequency  of  oscillation  of  a  Hertz  oscillator  is 
3,000,000  per  second,  find  the  length  of  the  waves  it  will  produce. 

Ans.  10,000  centimetres. 

6.  Explain  the  action  of  a  resonator. 

7.  Give  the  reasons  which  exist  for  thinking  that  light  is  an 
electromagnetic  phenomenon. 

8.  How  is  the  action  of  magnetic  forces  upon  the  direction 
of  the  vibrations  of  light  shown?  and  what  is  the  difference 
between  magnetic  and  diamagnetic  media  in  respect  of  their 
magneto-optic  properties  ? 

9.  It  was  announced  by  Willoughby  Smith  that  the  resist- 
ance of  selenium  is  less  when  exposed  to  light  than  in  the  dark. 
Describe  the  apparatus  you  would  employ  to  investigate  this 
phenomenon.    How  would  you  proceed  to  experiment  if  you 
wished  to  ascertain  whether  the  amount  of  electric  effect  was 
proportional  to  the  amount  of  illumination  ? 


INDEX 


N.B. —  The,  Numbers  refer  to  the  Numbered  Paragraphs. 


ABSOLUTE  Electrometer,  287 

Galvanometer,  213 

units,  353 

Accumulators,  492   (see  also    Con- 
denser) 

used  in  locomotion,  446 
Action  at  a  distance,  25,  64,  299 

in  medium,  5,  13,  64,  279,  299 
Aether  (see  Ether) 
Air  condenser,  56,  294,  359 
Air-gap,  378 

Air,  resistance  of,  313,  326 
Aldini,  Giovanni,  experiments  on 

Animals,  255 

Alternate  currents,  162,  461,  470 
Alternate  current  magnet,  388,  477 

method  of  measuring  resist- 
ance, 417 

motors,  484 

power,  475 
Alternators,  478 
Aluminium,  reduction  of,  494 
Amalgam,  electric,  44 

ammonium-,  sodium-,  etc.,  490 
Amalgamating  zinc  plates,  174 
Arnber,  2 

Amoeba,  the  sensitiveness  of,  256 
Ammeter,  221 

Ampere,  Andre  Marie,  Theory  of 
Electro-dynamics,  392 

"Ampere's  Rule,"  197,  382 

Laws  of  currents,  390,  391 

suggest  a  Telegraph,  497 

Table  for  Experiments,  391 

Theory  of  Magnetism,  398 
Ampere,  the,  162,  207,  354 

meter,  221 
Ampere-turns,  341,  377  (and  p.  595) 


Amplitude  of  E.M.F.,  470 
Angle  of  lag,  472,  473 
Angles.  Ways    of   Reckoning,   144, 
Appendix  A 

Solid,  148,  Appendix  A 
Animal  Electricity,  76,  257 
Anion,  239,  491 

Annual  variations  of  magnet,  157 
Anode,  170,  236 
Anomalous  magnetization,  373 
Aperiodic  galvanometer,  219 
Apparent  watts,  438,  472,  475 

resistance,  417e,  458c,  472 
Appropriating  brush,  50 
Arago,  Francois  Jean, 

classification      of      lightning, 
331 

on  magnetic  action  of  a  voltaic 
current,  202,  381 

on  magnetic  rotations,  457 
Arc,  the  electric,  theory  of,  448 
Arc  lamps,  449 

light,  448 

Arc-lighting  machines,  468 
Armature  of  magnet,  103 

of   dynamo-electric    machine, 

462 

Armstrong,  Sir  Wm.,  his  Hydro- 
electric Machine,  48 
Astatic  magnetic  needles,  201 

Galvanometer,  201,  211,  215 
Asynchronous  motors,  486 
Atmospheric  Electricity,  72,  328 
Atoms,  charge  of,  491  (footnote) 
Attracted-disk  Electrometers,  287 
Attraction    and    repulsion    of  elec- 
trified bodies,  2,  4,  22,  24, 
74,  262 


609 


610 


ELECTRICITY   AND   MAGNETISM 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Attraction  and  repulsion  of  currents, 
389 

and  repulsion  of  magnets,  84, 
88,  337 

due  to  influence,  24 
Aurora,  the,  158,  159,  161,  336 
Ayrton  (  W.  E.)  and  Perry  (John} 

ammeter,  221 

on  contact  electricity,  80 

on  dielectric  capacity,  298 

secohmmeter,  458  (c) 

value  of  "v,"  359 

voltmeter,  221 
Ayrton  and  Mather  galvanometer, 

216 
Azimuth  Compass,  149,  151 

B.  A.  UNIT,  358 

Back  E.M.F.,  445 

Back  Stroke,  29 

Bain,  Alex.,  his  Chemical  Writing 

Telegraph,  246 
Balance  methods,  139,  411, 413  et  seg. 

Wheat  stone's,  413 
Ballistic  Galvanometer,  218,  418 
Bancalari  on  flames,  374 
Barrett,  William  F.,  on  magnetic 

contraction,  124 
Batteries,  voltaic,  168,  179,  193 

list  of,  189 
secondary,  492 
Battery  of  Leyden  jars,  62 
Beccaria,  Father  G.,  on  electric 

distillation,  251 

on  atmospheric  electricity,  333 
Becquerel,  Antoine  Cesar,  on  atmo- 
spheric electricity,  334 
on  olamagnetism,  369 
Becquerel,  Edmond,  on  photo-vol- 
taic currents,  530 
Becquerel,  Henri,  on  magneto-optic 

rotation,  f>26 

Bell,  Alexander  Graham,  his  Tele- 
phone, 510 

Uses  induction  balance  to  de- 
tect bullet,  514 
The  Photophone,  f>'29 
Bells  electric,  508 
Bennct,  Abraham,  his  doubler,  49 

Electroscope,  16,  28 
Best  grouping  of  cells,  192,  407 
Bichromate  Battery,  180,  189 
Bidwell,  Shelford,  on  magnetic  con- 
traction, 124 
on  susceptibility,  365 
on  lifting  power,  384 
Effect  of  light  on  magnets,  524 


Bifilar  Suspension,  130,  209,  288 

Biot,    Jean   Baptiste,    experiment 

with  hemispheres,  33 
Law  of  magnetic  distribution, 

153 
on  atmospheric  electricity,  334 

Bismuth,  diamagnetic  properties  of, 

94,  370 

change  of  resistance  in  mag- 
netic field,  397 

Blasting  by  electricity,  316,  432 

Blood,  conducting  power  of,  256 

Board  of  Trade  Unit,  440 

Board  of  Trade  Standards,  Appen- 
dix B 

Bolometer,  404 

Boltzmann,  Ludwig,  on  Dielectric 
capacity,  297,  298,  518 

Boracite,  74 

Bosanquet,  R.  H.  M.,  magnetic  cir- 
cuit, 375 

"  Bound  "  electricity,  27,  79 

Boyle,  Hon.  Robert,  2  (footnote) 

Boys,  Charles  Vernon,  radio-micro- 
meter, 425 

Brake-wheel  arc  lamps,  449 

Branched  circuit,  409 

Brass,  deposition  of,  490 

Breaking  a  magnet,  116 

Breath-figures.  324 

Bridge,  Wheatstone's,  413 

British  Association  Unit,  358 

Broad  side-on  method,  138 

Brown,  C.  E.  L.,  on  motor,  486 

Brugmans  discovers  magnetic  re- 
pulsion of  bismuth,  369 

Brush,  Charles  F.,  his  dynamo,  468 

Brush  discharge,  319,  324 

Brushes,  463 

Bunsen's  Battery,  183,  1^9 

CABLE,  Atlantic, 301  (footnote),  802, 

323,  504 
submarine,  504 

"          as  condenser,  301, 
323 

Cabot,  Sebastian,  on  magnetic  de- 
clination, 151 

Cadmium  in  standard  cell,  188 
Cailletet  on  resistance  of  air,  313 
Calc-spar,  75 

Calibration  of  Galvanometer,  211 
Callan,  induction  coil,  229 

Battery,  183  (footnote) 
Callaifd's  Battery,  187 
Callender's  pyrometer,  404 
Calomel  cell,  188 


INDEX 


611 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Calories  and  joules,  427,  439 
Candles,  electric,  451 
Canton,  John,    discovers    electro- 
static induction,  22 

on  electric  amalgam,  44 
Capacity,  definition  of,  271 

in  alternate  circuit,  473 

measurement  of,  418 

of  cable,  301  et  seq. 

of  condenser,  58,  294,  304,  473 

of  conductor,  40,  55,  272,  304 

of  Leyden  jar,  58,  294 

of  liquid  condenser,  492 

specific  inductive,  25,  56,  295, 
304 

unit  of  (electrostatic),  272 

unit  of  (practical),  303 
Capillary  Electrometer,  253,  292 
Carbon   plates  and  rods,  183  (foot- 
note) filaments,  452 
Carbons  for  arc  lamps,  449 
Cardew,  Philip,  his  voltmeter,  430, 

471 
Carhart,   Henry  S.,  on    standard 

cells,  188 
Carnivorous     Plants,     sensitive    to 

electricity,  256 
Carre,  F.,  Dielectric  machine,  45 

on  magnets  of  cast  metal,  106 
Carriers,  49 
Cars,  electric,  446 
Cascade  arrangement  of  jars,  309 
Cautery  by  electricity,  431 
Cavallo,  'Tiberius,  his  attempt  to 
telegraph,  497 

his  pith-ball  electroscope,  4 

on  atmospheric  electricity,  333 
Cavendish,  Hon.  H.,  on  Specific  In- 
ductive capacity,  295,  296 

on    nitric   acid    produced    by 

sparks,  316 

Ceca,  Father,  on  atmospheric  elec- 
tricity, 333 
Cell,  voltaic,  166 
Cells,  classification  of,  180 

grouping  of,  192,  407 

list  of,  189 

Centi-ampere  balance,  396 
Central  stations,  440,  478 
Circuit,  166,  406 

Magnetic,  375 

points  of,  where  energy  gained 

and  lost,  248,  436 
Circuits,  branched,  243,  409 
Circuital  magnetism,  118,  347 
Circular  current,  345 
City  of  London  central  station,  478 


Change  of  configuration,  law  of,  204, 

379 

Characteristic  curves,  466 
Charge,  electric,  8 

resides  on  surface,  32 
residual  of  Leyden  jar,  61,  299 
of  accumulator,  492 
Chart,  magnetic,  154  (frontispiece) 
Chemical  action,  E.M.F.  of,  488 
Chemical  actions  in  the  battery,  172 
laws  of,  178,  240,  488 
of  spark  discharge,  316 
outside  the  battery,  234,  487 
Chemical    test   for  weak    currents, 

246,  316 

depolarization,  180 
Chimes,  electric,  46 
Choking-coils,  474 
Choking  effect,  459,  473,  474 
Chromic  solution,  183 
Chronograph,  electric,  509 
Clamond's  thermopiles,  425 
Clark,  Latimer,  his  standard  cell, 

188,  and  Appendix  C 
Classification  of  cells,  180 
Clausius,  R.,  theory  of  Electrolysis, 

491 

Cleavage,  electrification  by,  68 
Clock  diagram,  470,  472 
Clocks,  electric,  509 
Closed  circuit,  cell  for,  176,  181 
Closed -circuit  method  of  Telegraphy, 

500 

Closed-coil  armature,  463 
Cobalt,  magnetism  of,  93 
Coefficient  of  Magnetic  induction 

(see  Permeability) 
of    Magnetization    (see    Sus- 
ceptibility) 

of  mutual-induction  (or  poten- 
tial), 351,  454 
of  self-induction,  458 
Coercive  force,  96,  367 
Colour  of  spark,  318 
Columbus,  Cristofero,  on  magnetic 

variation,  151 

Combs  on  influence  machine,  42,  50 
Combustion  a  source  of  electrifica- 
tion, 70 
heat  of,  488 
Commercial   efficiency  of  d3rnamo, 

464 

Commutator,  443,  461,  463 
Compass  (magnetic),  Mariner's,  87, 

149 

error  due  to  iron  ship,  149 
Compound  circuit,  192,  243,  409 


C12 


ELECTRICITY  AND   MAGNETISM 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Compound  dynamo,  465,  467 

magnets,  104 
Condensation,  56 
Condenser,  56,  294,  303 

capacity    of,    how    measured, 
418 

discharge  of,  326,  515 

in  alternate  circuit,  473,  474 

liquid,  492 

method  of  measuring  a  resist- 
ance, 411,  417 

standard,  303 

use  of,  229,  302 
Condensing  electroscope,  79 
Conductance.  402,  404 
Conduction,  7,  30,  171,  402,  404,  476 

by  liquids,  234,  404 

of  gases,  171,  322 
Conductivity,  171,  322,  346,  348,  402, 

404 
Conductor   cutting  lines,  225,  339, 

353,  355 
Conductors  and  Non-conductors,  8, 

27,  30,  402  et  seq. 
Conductors  electrified  by  rubbing,  13 

opaque,  518 

Consequent  Poles,  117,  120,  382 
Constant-current  dynamos,  468 

voltage  dynamos,  467 
Contact  Electricity,  79,  163 

Series  of  metals,  80 

rings,  461 

of  surfaces,  12 

Continuous-alternate    transformers, 
483 

currents,  162 

current  dynamos,  463 

current  transformers,  482 

electrophorus,  26,  49 
Contraction  due  to  magnetism,  124 
Control  of  galvanometer,  209 
Convective  discharge,  312 
Convexion  of  electricity,  49,  312,  397 

currents,  397 

induction    machines  (see  In- 
fluence machines) 

streams  at  points,  38,  47,  274, 

329 

Cooking  by  electricity,  434 
Cooling  and  heating  of  junction  by 

current,  419 

"  Corkscrew  Eule,"  198 
Cost  of  power  derived    from   elec- 
tricity, 440 
Coulomb,  Torsion  Balance,  18, 132 

Law  of  Inverse  Squares,  19, 
129,  132,  261,  270 


Coulomb  on  distribution  of  charge, 

38,  273 
Coulomb,  the,  162,  354 

how  many  electrostatic  units, 

262  (footnote} 
Couple,  magnetic,  136 
Coupling  of  alternators,  479 
Creeping,  stopped  by  paraffin,  183 

magnetic,  368 
CrooJces,  William,  on  shadows  in 

electric  discharge,  321 
on    repulsion    from    negative 

electrode,  327 
Crown  of  cups,  165 
Cruickshank's  Trough  Battery,  180 
Crystallization,  69 
Crystals,  electricity  of,  74,  75 

dielectric  properties  of,  297 
magnetism  of,  373 

Gumming,  James,  invents  galvan- 
ometer, 200 

thermo-electric  inversion,  423 
Cuneus"1  discovery  of  Leyden  jar,  60 
Curbing  telegraphic  signals,  302 
Current,  effects  due  to,  167 
Electricity,  162 
strength  of,  171,  190 

unit  of,  162,  207 

Current,  is  the  magnetic  whirl,  202 
balance,  396,  and  Appendix  B 
sheets,  410 
Currents,  very  large,  measurement 

of,  412 
Curvature    affects    surface-density, 

88,  274 

Curve-tracer,  368 
Curves,    magnetic   (see    Magnetic 

Figures) 
Curves  of  magnetization,  364 

characteristic  of  dynamos,  466 
Cuthbertson,    John,    his     electric 

machine,  41 
Cycles  of  magnetization,  368 

of  alternate  currents,  470 
Cylinder  Electrical  machine,  42 

DAILY  variations  of  compass,  156 
Dalibard's  lightning-rod,  329 
Damping  galvanometers,  219 
Darnell,  John  P.,  his  cell,  181,  184 
D'Arsonval.  galvanometers,  216 
Davy's  (Marie)  Battery,  193 
Davy,   Sir    Humphry,   magnetiza- 
tion by  current,  381 
discovers  electric  light,  448 
electrolyses    caustic    alkalies, 
490  (c) 


INDEX 


613 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


De  Haldat,  magnetic  writing,  122 
De  la  Rive's  Floating  Battery,  205 
De  la  Rue,  Chloride  of  Silver  Battery, 
186,  313 

on  electrotyping,  495 

on  length  of  spark,  313 
Dead-beat  galvanometers,  219 
Declination,  Magnetic,  151 

variations  of,  151,  155 
Decomposition  of  water,  235 

of  alkalies,  490  (o) 
De-electrification  by  flame,  314 
Deflexions,  method  of,  131,  136 
Deflexion  of  galvanometer,  210 
Dellmami's  electrometer,  286 
Demagnetize,  how  to,  368 
Density  (surface)  of  charge,  38,  2T3, 

magnetic,  134,  337 
Depolarization,  mechanical,  180 

chemical,  180,  182,  183 

electro-chemical,  180,  181 
Deposition  of  metals,  494 
Deviation  of  compass,  149 
Dewar,   James,    on   currents    gen- 
erated by  light  in  the  eye, 
257 

his  capillary  electrometer,  253 

magnetic  properties  of  iron  at 
200°,  111 

oxygen,  magnetic,  370 
Dewar  and  Fleming,  resistance  at 

low  temperature,  404 
Diagram,  thermo-electric,  424 
Dial  bridge,  415 
Diamagnetic  polarity,  369 
Diamagnetisrn,  94,  369 

of  flames,  374 

of  gases,  370,  374 
Diaphragm  currents,  254 
Dielectric  capacity,  295  to  299 

capacity,  effect  on  intensity  of 
field,  262,  298 

coefficient,  283,  517 

strength,  315 
Dielectrics,  10,  25,  57,  295 
Difference  of  potential,  265 

magnetic  potential,  337 
Differential  galvanometer,  217,  411 
Dimensions  of  units,  356 
Di-phase  currents,  485 
Dip,  or  Inclination,  152 

variation  of,  155 
Diplex  signalling,  503 
Dipping  Needle,  152 
"Direct"  and   "inverse"   current, 

223 
Direction  of  induced  E.M.F.,  226>450 


Discharge  affected  by  magnet,  322 

brush,  319,  324 

by  evaporation,  251 

by  flame,  8,  314 

by  points,  47,  319,  329 

by  water  dropping,  334 

conductive,  310 

convective,  47,  312 

disruptive,  311 

effects  of,  47,  315,  316,  317 

glow,  319,  329  (footnote) 

limit  of,  273 

oscillatory,  515 

sensitive  state  of,  322 

striated,  320 

through  gas   at  low  voltage, 
322 

velocity  of,  323 
Discharger,  Discharging-tongs,  59 

Universal,  62 
Disk  armature,  463 
Displacement,  electric,  57 

currents,  516 

Disruption,  electrification  by,  68 
Dissectible  Leyden  jar,  63 
Dissipation  of  Charge,  326 
Dissociated  gases  conduct,  322 
Distillation,  electric,  251 
Distribution  of  Electricity,  31  to  38, 
273,  274 

of  Magnetism,  117,  134 
Distribution  by  transformers,  480 
Distribution  of  energy,  440 
Distortion  of  dynamo-field,  463 
Divided  circuits,  409 

Touch,  101 
Dolbear,  A.  E.,  his  telephone,  299, 

510 

Doubler,  the,  26,  49 
Double  refraction  by  electric  stress, 

524,  525 

Double  Touch,  102 
Dreh-strom,  485 

Drop  of  voltage  in  mains,  412,  447 
Dry  cells,  184,  189,  193 
Dry-Pile,  193,  291 
Du  Bois,  limit  of  magnetization,  363 

measurement  of  permeability, 

366 

Duboscq,  Jules,  his  lamp,  449 
Du  Fay's  experiments,  5,  30 
Duplex  Telegraphy,  302,  503 
Duration  of  Spark,  323 
Dust,  allaying,  54 
Duter  on  Electric  Expansion,  300 
Dynamic  Electricity  (see    Current 
Electricity) 


614 


ELECTRICITY   AND   MAGNETISM 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Dynamos,  461 

as  motors,  443,  463 
Dynamometer,  394 
Dyne,  the  (unit  of  force),  281 

EARTH,  the,  a  magnet,  95 

currents,  302 

electrostatic  capacity  of,  303 

intensity  of  magnetization,  365 

magnetic    force    in    absolute 
units,  361 

used  as  return  wire,  49T 
Earth's  magnetism  (see  Terrestrial 

Magnetism) 
Earth,  potential,  269 
Ebert,  H.,  on  oscillations,  522 
Eddy-currents,  457,  477,  486 
Edison,     Thomas    Alva,     electric 
lamp,  452 

carbon  telephone,  511 

meter  for  currents,  244,  442 

quadruplex  telegraphy,  503 
Edlund  on  galvanic  expansion,  249 
Eel,  electric  (Gymnotus),  76 
Efficiency  of  transmission,  447 

of  dynamos,  464 

of  motors,  445 

of  transformers,  481 
Electric  Air-Thermometer,  317 

Cage,  37 

Candle,  451 

Clocks,  509 

Displacement,  57 

Distillation,  251 

Egg,  the,  232,  320 

Expansion,  300 

Field,  13,  16,  20,  22,  24,  262, 
279,  299,  524,  525 

Force,  169  (footnote),  266 

(Frictional)  machines,  42 

Fuze,  316,  429,  432 

Images,  275 

Kite,  329 

Light,  448 

Lines  of  Force,  13,  16,  20,  22, 
24,299 

Mill  or  Fly,  47 

Oscillations,  515 

Osmose,  250 

Pistol,  316 

Shadows,  321 

Shock.  254 

Stress,  13,  16,  20,  22,  24,  63, 
279 

Waves,  515 

Wind,  47,  324 
Electrics,  2 


Electricity,  theories  of,  7,  327 

word  first  used,  2  (footnote) 
Electro-capillary  phenomena,  253 
Electro-chemical  Depolarization,  ISO 

equivalents,  240,  489 

power  of  metals,  489 
Electro-chemistry,  487 

deposition,  494 
Electrodes,  236 

unpolarizable,  257 
Electrodynamics,  389 
Electrodynamometer,  394 
Electrolysis,  237,  487 

in  discharge,  322 

laws  of,  240,  490 

of  copper  sulphate,  238 

of  water,  236,  487 

theory  of,  491 
Electrolytes,  236,  487 
Electrolytic  condenser,  492 

convexion,  491 
Electromagnet,     alternate    current, 

477 
Electromagnets,  107,  381 

laws  of,  380 

calculations  for,  375,  376  (and 

see  p.  595) 

Electromagnetic    engines  (see    Mo- 
tors) 

Electromagnetic    systems,    law    of, 
204,  379 

system  of  units,  852 

theory  of  Light,  517 

waves,  515 

Electromagnetics,  337 
Electromagnetism,  337 
Electrometallurgy,  494 
Electrometer,  absolute,  287 

attracted-disk,  287 

capillary,  253,  292 

Dellmanris,  286 

Peltier's,  2S6,  33^ 

portable,  287 

quadrant  (Lord  Kelvin's),  288 

repulsion,  286 

torsion,  18 

trap-door,  287 
Electromotive-force,  169,  487 

induced,  222 

measurement  of,  416 

unit  of,  854 

Electromotive  intensity,  266,  283 
Electromotors,  443,  484 
Electro-Optics,  524 
Electrophorus,  26 

continuous,  26,  49 
Electroplating,  496 


INDEX 


615 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Electroplating,  dynamos  for,  462 
Electroscopes,  14 

BenneVs  gold-leaf,  16,  28 

Bohnenberger's,  16,  291 

Fechner's,  291 

Gilbert's  straw-needle,  15 

Hankel's,  291 

Henlet/'s  quadrant,  17 

Pith-ball,  3,  4 

Volta's  condensing,  79 
Electroscopic  powders,  31,  47,  299, 

324 
Electrostatic  Optical  Stress,  525 

voltmeter,  290 
Electrostatics,  8,  259 
Electrotyping,  495 
Element  of  Current,  344 
Elwell  Parker  alternator,  478 
End-on  method,  138 
Energy,  1,  64 

of  magnetic  field,  202 

of  charge  of  Leyden  jar,  305 

of  electric  current,  435 

paths,  518 

points  in   circuit  where  it  is 
lost  or  gained,  248,  436 

supply  and  measurement  of, 

Equator,  Magnetic,  86 
Equipotential  surfaces,  267 

magnetic,  337  (f) 

Equivalents,  electro-chemical,  240 
Erg,  the  (unit  of  work),  281 
Ether,  1,  7,  64,  517 
Evaporation  produces  electrification, 

71,  330 

discharge  by,  251 
Everett,  James  D.,  on  atmospheric 

electricity,  334 

on   exact  reading   of  galvan- 
ometer, 214  (footnote) 
on  intensity  of  magnetization 

of  earth,  365 

Ewing,  James  A.,  on  limit  of  mag- 
netization, 363 

curves  of  magnetization,  364 
theory  of  magnetism,  127 
Exchanges,  telephone,  513 
Excitation  of  Field-magnets,  465 
Exciting  power,  377 
Expansion,  electric,  300,  525 
Extra-current,  459 

FAILURE  and  exhaustion  of  bat- 
teries, 172 

Fall  of  potential  along  a  wire,  289, 
412 


Farad,  the  (unit  of  capacity),  303, 354 
Faraday ,  Michael,  molecular  theory 

of  electricity,  7 
chemical  theory  of  cell,  178 
dark  discharge,  319 
diamagnetism,  369,  373,  374 
discovered  inductive  capacity. 

25,  296,  298 

discovery  of    magneto-induc- 
tion, 222 

Disk  machine,  227 
electromagnetic  rotation,   393 
experiment  on   dielectric  po- 
larization, 299 
gauze-bag  experiment,  34 
hollow-cube  experiment,  34 
ice-pail  experiment,  37 
laws  of  electrolysis,  240,  242 
length  of  spark,  313 
Magnetic  lines-of-force,  119 
magnetism  in  crystals,  373 
on  Arago's  rotations,  457 
on  dissipation  of  charge,  314 
on  electrodynamics,  392 
on  identity  of  different  kinds 

of  electricity,  245,  246,  316 
predicted    retardation    in    ca- 
bles, 301 
Ring,  228 
rotation  of  plane  of  polarized 

light,  526 
voltameter,  242 

Faure,  Camille,  his  Secondary  Bat- 
tery, 492 
Favre's    experiments    on    heat    of 

currents,  428 

Fechner's  electroscope,  291 
Feddersen,   W.,  on  electric  oscilla- 
tions, 514 
Feeders,  440 

Ferromagnetic  substances,  369 
Field,  electric,  13,  16,  20,  22,  24,  262, 

279,  299,  525 

magnetic,  115, 202,  337, 462, 526 
Field-magnet,  462 
Field-magnets,  excitation  of,  465 
Field-plate,  50 
Figures,    magnetic    (see    Magnetic 

Figures) 

electric,  31,  299,  324 
Filament  of  incandescent  lamps,  452 
Filings  for  mapping  fields,  121 
Fire  of  St.  Elmo,  329  (footnote) 
Flame,  currents  of,  314 

diamagnetism  of,  374 
discharge  by,  8,  814 
produces  electrification,  70 


616 


ELECTRICITY   AND   MAGNETISM 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


"Flashing"  filaments,  452 
Fleming  and  Dewar,  resistance  at 

low  temperature,  404 
Fleming,  John  Ambrose,  his  Bat- 
tery, 193 
rule  as  to  direction  of  E.M.F., 

226 
Flux,  magnetic,  142,  887,  368,  377 

density,  363  (footnote) 
Fontana  on  electric  expansion,  300 
Force,  electric,  169  (footnote),  266, 

276,  277 

electromotive  (see  Electromo- 
tive-force) 
magnetic,  91,  169  (footnote), 

near  a  straight  conductor,  207, 

843 

on  conductor  in  field,  840,  341 
Form,  effect  of,  on  retentivity,  98 

on  lifting  power,  114 
"Forming"  accumulator  plates,  492 
Foster,  George  Carey,  his  evalua- 
tion of  ohm,  358 
method  of  testing,  415 
Foucault,    Leon,     his     Regulator 

Lamp,  449 
Interrupter,  229 

Foucault-currents  (see  Eddy-cur- 
rents) 

Franklin,  Benjamin,  discovered  ac- 
tion of  points,  mentioned  in, 
88  (c),  47,  329 

cascade  arrangement  of  Ley- 
den  jars,  809 
Electric  chimes,  47 
Electric  kite,  829 
Electric  portraits,  317 
his  charged  pane  of  glass,  55 
invents  lightning  conductors, 

329,  332 
kills  turkey  by  electric  shock, 

254 

One-fluid    theory    of    electri- 
city, 7 

on  seat  of  charge,  63 
theory  of  the  aurora,  336 
Frankfort,  "transmission    of    power 

to,  447,  ^5  (footnote) 
"  Free  "  electricity,  27,  79  (footnote) 
Frequency,  470,  476 

of  oscillations,  515,  520 
Friction  produces  electrification,  2, 12 
Frog's  legs,  contractions  of,  163,  255 
Frolich,  Otto,  on  electromagnet,  380 
Froment's  motor,  448 
Fuel,  zinc  as,  166 


Fuses,  316,  429,  432 
Fusing  of  wires,  429 


"  G  "  of  galvanometer,  213 
Galvani,  Aloysius.  observed  move- 
ments of  frog's  leg,  163 
on  preparation  of  frog's  limbs, 

on  Animal  Electricitv,  257 
Galvanic  Batteries  (see  Voltaic  Bat- 
teries) 

Electricity  (see  Current  Elec- 
tricity) 
Taste,  254 

Galvanism    (see    Current   Electri- 
city) 

Galvanometer,  208 
absolute,  213 
astatic,  211,  215 
ballistic,  218,  418 
constant  of,  '213 
damping  of,  219 
D^Arsonval's,  216 
dead  beat,  219 
differential,  217,  411 
Du  Bois  fteymond's,  257 
reflecting  (Lord  Kelvin's),  or 

mirror,  215 
sine,  214 
tangent,  212 

Von  Helmholtz's,  212  (foot- 
note) 

Galvanoplastic  (see  Electrotyping) 
Galvanoscope,  199 
Gas  Battery,  493 
Gases,  dissociated,  conduct,  822 
resistance  of,  171,  314,  322 
Gassiot,  J.  P.,  on  strife,  322,  327 
Oaugain,  Jean  Mothee, 

on  Pyroelectricity,  74 
Tangent    Galvanometer,     212 

(footnote) 
Gauss,    C.   F.,   invented    absolute 

measurement,  852 
magnetic  force  of  the  earth, 

861 

magnetic  observations,  365 
on  magnetic  shell,  848 
Gay-Lussac,  on  atmospheric  elec- 
tricity, 334 
Geissler's  tubes,  320 
Generators  of  alternate  currents,  473 

continuous  currents,  463 
Gernez  on  electric  distillation,  251 
Gibson  and  Barclay  on  dielectric 
capacity  of  paraffin,  297 


INDEX 


617 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Gilbert,    Dr.    William,    discovers 

electrics,  2 
discovered  magnetic  reaction, 

91 
discovers  that  the  earth  is  a 

magnet,  95, 150 
heat     destroys      magnetism, 

109 

his    balanced  -  needle    electro- 
scope, 15 
his  terrella,  95 
observation  of  moisture,  10 
observations  on  magnets,  86 
on  de  -  electrifying    power  of 

flame,  314 

on  magnetic  figures,  119 
on  magnetic  substances,  92 
on  magnetic  permeability,  97 
on  methods  of  magnetization, 

105,  106 

Glass,  a  conductor  when  hot,  31 
Globular  lightning,  331 
Glow  Discharge,  319,  329  (footnote) 

lamps,  452 

Gold-leaf  Electroscope  (see  Electro- 
scope) 
Gordon,  J.  E.  ff.,  on  magneto-optic 

rotatory  power,  526 
on    dielectric    capacity,    297, 

298 

on  length  of  spark,  313 
Gramme,   Zenobe    Theophile,    his 

ring-armature,  463 
Gravity  Battery,  187 
Gray,  Andrew,  Absolute  Measure- 
ments in    E.   and    M.,   136 
(footnote),  287  (footnote), 
396  (footnote) 

Gray,  Stephen,  discovers  conduc- 
tion, 30 

on  lightning,  829 
Grid  of  accumulator,  492 
Grotthuss'  theory,  172,  491 
Grouping  of  arc  lamps,  450 
cells,  192,  407 
glow-lamps,  453 
Grove,   Sir   William  R.t  his  Gas 

Battery,  493 
Grove's  Battery,  182 
magnetic  experiment,  124 
on  electric  property  of  flame, 

814 

Guard-ring,  Guard-plate,  273,  287 
Guericke,     Otto    von,    discovered 

electric  repulsion,  4 
invents  electric  machine,  41 
observes  electric  sparks,  11 


Gunpowder  fired  by  electricity,  316, 

317,  432 
Guthrie,  Frederick,  effect  of  heat 

on  discharge,  314 
heating  of  kathode  in  water, 

433 
Gymnotus  (electric  eel),  76,  246 

HALF  deflexion  method,  417 
Hall,  Edward  H.,  his  effect,  397 
Hankel,    Wilhelm   G.,   his  electro- 

scope, 291 

Hardening  of  steel,  108 
Harris,   Sir    W.    Snow,   his   unit 

Leyden  jar,  285 
attracted  -'disk     electrometer, 

287 

on  length  of  spark,  313 
Hauksbee,    Francis,    on    thunder- 

storms, 329 
Haily.  The  Abbe,  his  astatic  method, 

201 

Heat  and  resistance,  426,  439 
of  combination,  488 
effect  of,  on  magnets,  109,  111 
"  batteries,  194 


"  resistance,  404 

emission,  386,  429 
Heat,  unequal  action  of,  on  -I-  and  — 

charges,  314,  327 
Heating  of  coils,  386,  429 
Heating  effects  of  currents,  182,  426, 

439 

due  to  magnetization,  124,  368 
effect  of  sparks,  817 

"         dielectric  stress,  299 
local,  at  electrodes,  491 
Heaviside,  Oliver,  reluctance,  375 

(footnote) 
on  energy  paths,  518 
on  quadruplex  telegraphy,  497 
Helmholtz,  Hermann  L.  F.  von,  on 
effect  of  current  on  sight, 
254 

Electrolytic  convexion,  491 
Equations    of    self-induction, 

460 

Galvanometer,  212  (footnote) 
Hemihedry  in  crystals,  75 
Henry,  Joseph,  invented  the  "  soun- 

der," 497 
on  induced  currents  of  higher 

orders,  455 

Henry,  the,  854,  454,  458 
Hertz,  Heinrich,  on  effect  of  ultra- 
violet waves,  818,  681 


618 


ELECTRICITY   AND   MAGNETISM 


The  Numbers  refer  to  the  Numbered  Paragraphs 


Hertz,  Heinrich,  kathode  rays,  321 
researches  on  electric  waves, 

520 

Heydweiller,  on  length  of  spark,  313 
Hittorf,  on  discharge,  322 
High  frequency,  476,  515,  520 
Holtz,  W.,  his  electric  machine,  53 
on  electric  shadows,  321 
on    tubes    having    unilateral 

resistance,  327 

Hopkinson,  John,  on  dielectric  ca- 
pacity of  glass,  297 
on    residual    charge    and    its 

return,  299 
on  magnetization,  364 
his  characteristic  curves,  466 
Horizontal  component  of  magnetism, 

136,  153,  361 

Horse-power  and  watts,  435 
Hot  glass,  a  conductor,  31 
Hughes,  David  Edward,  the  Print- 
ing Telegraph,  497 
the  Microphone,  512 
magnetic  balance,  140 
induction  balance,  514 
Humboldt,  Alexander  von,  on  elec- 
tric eels,  76 

discovers  galvanic  smell,  254 
produced  electric  contractions 

in  fishes,  255 

Hunter,  Dr.  John,  on  effect  of  cur- 
rent on  sight,  254 
Hydroelectric  machine,  48 
Hysteresis,  367,  368 


IDIOSTATIO  method    of  using  volt- 
meter, 290 
Images,  electric,  275 
Impedance,  472 
(Impedance)  coils,  474 
Incandescent  lamps,  452 
Inclination  (or  Dip),  152 

variation  of,  155 
Index  Notation,  355 
Inductance,  458 
Induced  charges  of  electricity,  22 

currents,  222 
Induction  (electrostatic)  of  charges, 

(see  Influence) 
(magnetic)  linos  of,  96 
(magnetic)  of  magnetism,  96 
(magneto-electric)     of     cur- 
rents, 222 

(volta-electric)  of  currents  by 
currents  (see  Self  induc- 
tion, Mutual  induction) 


Induction,  the,  meaning  the  internal 
magnetization,  363  (foot- 
note) 

Induction-coil  or  Inductorium,  229 

Induction-convexion  machines,  49 

Inductive-capacity,  specific,  25,  56, 
295,  299 

Inertia,  electromagnetic,  458 

Influence,  22 

Influence-machine,  49-54 

Insulators,  10,  30,  405 

Intensity  of  current,  190  (footnote) 
of  earth's  magnetic  force,  153, 

358,  361 

of  magnetic  field,  338 
of  magnetization,  365 

Internal  resistance,  171,  406,  417 
of  armatures,  462 

International  ohm,  358 

"Inverse"  and  "direct"  currents, 
223 

Inverse  Squares,  Law  of,  19,  129. 
148,  261,  270 

Inversion,  Thermo-electric,  423 

Ions,  239 

Ironclad  magnet,  383 

Iron,  properties  of,  362 

Iron  rods  red  hot  in  water,  433 

Isoclinic  lines,  154 

Isogonic  lines,  154 

Isolated,  271 


JABLOCHKOFF,  PAUL,  his  battery, 

193 

electric  candle,  451 
Jacobi,  Moritz  Hermann,  on  local 

action,  174 

discovers  galvanoplastic   pro- 
cess, 495 

his  boat  propelled  by  electri- 
city, 443 

on  electromagnet,  380 
theory  of  electromotors,  443 
Jar,  Leyden,  59 

capacity  of,  58, 294, 804 
"        cascade     arrangement 

of,  309 
discharge  of,  59,  310, 

515 

discovery  of,  60 
"   energy  of  charge  of, 

305 
"   seat  of  charge  of,  63 

spark  of,  318,  323 
"   theory  of,  294 
Unit,  285 


INDEX 


619 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Jenkin,  Fleeming,  on  cable  as  con- 
denser, 301 

on  retardation  in  cables,  323 
Joints  in  magnetic  circuit,  378 
Joule,  James  Prescott,  on  effects  of 

magnetization,  124 
evaluation  of  ohm,  358 
Law  of  heat  of  current,  427, 

439 

limit  of  magnetization,  363 
magnetic  circuit,  375 
Mechanical  equivalent  of  heat, 

439,  488 
on     atmospheric     electricity, 

333 

on    lifting-power    of    electro- 
magnet, 3S4 
Joule  effect,  420 
Joule,  the,  354,  439 

KA.PP,  GISBERT,  on  magnetic  circuit, 

377 

Kathode,  170,  236 
Kathodic  "rays,"  321 
Ration,  239,  491 
Keeper,  103 

Kelvin,  Lord  (Sir  William  Thom- 
son) 
Attracted-disk    Electrometer, 

79,  287 
Compass,  149 
Current  Balances,  396 
Divided  ring  Electrometer,  79 
Electric    convexion     of    heat 

(Thomson  effect),  424 
Evaluation  of  ohm,  358 

"      "v,"359 

Modified  Daniell's  cell,  187 
on  atmospheric  electricity,  333 
on  electric  images,  275 
on    electrostatics,  287    (foot- 
note) 

on  length  of  spark,  313 
on  nomenclature  of  magnetic 

poles,  89  (footnote) 
on  sounds  in  condensers,  299 
predicts    electric    oscillations, 

515 
proof  of  contact    electricity, 

79 

Quadrant  Electrometer,  288 
Keplenisher  (or  Mouse  Mill), 

49,  287,  288 

Thermo-electric  diagram,  424 
Water-dropping  Collector,  334 
Kerr,  Dr.  John,  Electro-optic  dis- 
coveries, 800,  525 


Kerr,  Dr.  John,  Magneto-optic  dis- 
coveries, 125,  366,  527 

Kerr's  effect,  527 

Kinnersley,  Elijah,  Electric  Ther- 
mometer, 317 

Kirchhoff,       Gustav.       Laws       of 
Branched   Circuits,   409 

Kite,  the  electric,  329 

Kohlrausch,  Friederich,  on  resid- 
ual charge,  299 
on  electro-chemical  equivalent, 

240 
on  evaluation  of  ohin,  358 

Kundt,  August,  his  effect,  528 


LAG  and  lead,  472 

Lagging  of  magnetization,  368 

Lamellar  magnetization,  118 

Laminated  magnets,  104 

Lamination  of  cores,  457, 463, 477, 480 

Lamps,  arc,  449 

Lamps,  incandescent,  452 

Langley,  S.  P.,  his  bolometer,  404 

Law,  cell,  180 

Laws  of  electrolysis,  490 

of  inverse    squares,    19,    129, 
148,  261,  270 

of    electro-magnetic     system, 

204,  379 
Lead,  used  in  accumulators,  492 

no  Thomson-effect  in,  424 
Lead  and  lag,  in  phase,  472 
Lead  of  brushes,  463 
Leakage,  magnetic,  377 

photoelectric,  531 

rate  of  electric,  326 
Le  Bailliff,  diamagnetisrn,  369 
Leclanche,  Georges,  his  cell,  184 
Lemonnier   discovers    atmospheric 

electricity,  333 

Lenard,  Philipp,  aluminium  "  win- 
dow," 321 

Length  of  spark,  313 
Lenz's  Law,  456 
Lenz  on  electromagnet,  880 
Leyden  jar,  55 

prevention  of  piercing  spark, 
62 

oscillatory  discharge  of,  515 

resonance  between  two,  517 

seat  of  charge  in,  63 
Lrvdeiis  (see  Condensers) 
Lichtenberg's  figures,  324 
Life  of  Lamps,  452 
Lifting-power  of  magnets,  113,  114 

of  electromagnets,  884 


ELECTRICITY   AND   MAGNETISM 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Light  affects  resistance,  529 
affects  a  magnet,  524 
Electric,  488 
Electromagnetic  theory  of,  1, 

518 
polarized,  rotated  by  magnet, 

125,  526,  527,  528 
velocity  of,  359,  518 
Lightning,  11,  329,  331 
Lightning  conductors,  35,  832 
duration  of,  323,  331 
best    methods    of    protection 

from,  332 
Limit  of  heating  of  electromagnet, 

386 

magnetization,  363 
Lines-of-force,  electric.  13,  16,  20,  22, 

24,  268 

magnetic,  96,  119,  33T 
Line-integral,  341  (footnote) 
Lippmann,    G.,   Capillary  Electro- 
meter, 253,  292 
Liquids  as  conductors,  234,  490,  518 

resistance  of,  403,  404 
Liquid  condensers,  492 
"  Local  Action  "  in  batteries,  178 
Locomotion,  electric,  446 
Lodestone,  84 

Lodge,  Oliver,  on  resonance,  517 
his  oscillator,  521 
his  detector  or  coherer,  521 
London,    city    of,    Central    Station, 

478 

"  Long  "  and  "  short  "  coils  for  mag- 
nets, 386 
Long   and   short  coil  instruments, 

408 
Lorenz,  L..  on  evaluation  of  ohm, 

358 

Loss  of  charge,  326,  531 
Louis  XV.  electrifies  700  monks,  254 
Lullin's  experiment,  315 
Luminous  effects  of  spark,  318 

MACHINE,  Electric,  42 

alternate-current,  478 

cylinder,  42 

dynamo-electric,  461 

fioltz's,  53 

hydro-electrical,  48 

influence,  49 

magneto-electric,  461 

plate,  43 

Toepler's  or  Voss,  51 

Wimshurst,  52 

Winter's,  43 
Magne-crystallic  action,  373 


Magnet,  breaking  a,  116 

Magnets,   natural  and  artificial,  84, 

85 
Magnetic    actions    of  current,    195, 

338,  389 
attraction  and  repulsion,   88, 

121,  389 
cage,  97 
creeping,  368 
Magnetic  circuit,  375 

field,  115,  202,  389 

"     rotatory,  485,  486 
figures,  119,  120, 121,  202,  389 

"        theory  of,  142 
flux,  337,  377 

flux  density,  363  (footnote) 
force,  91,  337  (a) 

"      measurement  of,  130 
hysteresis,  367,  368,  464 
induction,  96,  363  (footnote) 
iron-ore,  84 
lag,  alleged,  368 
lines-of-force,  96,  119,  120,  121, 

349,  362,  373,  377,  389,  464 
lines-of-force  of  current,  202, 

389 

maps,  154 
meridian,  151 
metals,  93,  362,  369 
model  (Swing's),  127 
moment,  135,  346,  361 
needle,  87,  149 

oxide  of  iron,   84,  183  (foot- 
note) 

paradox,  a,  143 
permeability,  96,  363,  866,  518 
pole,  unit,  141,352 
potential,  337,  347,  848 
proof-plane,  232 
saturation,  112,  363 

"         JBeetz,  on,  126 
screen,  97 
shell,  118,  203,337  (A),  348 

"     force  due  to,  345 

"     potential  due  to,  348 
storms,  158,  336 
substances,  92,  362,  869 
susceptibility,  365 
units,  352 
writing,  122 
Magnetism,  84 

action  of,  on  light,  125,  126 

destruction  of,  109 

distribution  of,  117 

lamellar,  118 

laws  of,  89,128,  837 

of  gases,  370,  374 


INDEX 


621 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Magnetism,  permanent,  98 

phenomenon  of  rotation,  526 

residual,  112,  364 

solenoidal,  118,  347 

temporary,  98,  112 

terrestrial,  95,  150 

theories  of,  99,  126,  526 

unit  of,  141,  352 
Magnetite,  84 
Magnetization,  anomalous,  373 

coefficient  of  (see    Suscepti- 
bility) 

cycles  of,  367,  368 

intensity  of,  365 

lamellar,  118 

mechanical  effects  of,  124 

methods  of,  100-107 

solenoidal,  118,  347 

sound  of,  124,  510 

time  needed  for,  388 
Magneto-electricity,  82,  222,  461 
Magneto-electric  machines,  461 
Magnetographs,  160 
Magnetometer,  137 

self-registering,  160 
Magnetomotive-force,  341,  375 
Magneto-optic  Rotations,  524 
Magnets,  see  also  electromagnet 

action  of  light  on,  524 

artificial,  85 

compound,  104 

forms  of,  103 

lamellar,  118 

laminated,  104,  477 

methods  of  making,  100-107 

natural,  84,  103 

power  of,  114 

unvarying,  110 

Mance,  Sir  Henry,  his  method,  417 
Manganese  steel,  363 
Manganin,  404 
Maps,  magnetic,  154 
Mariner's  Compass,  149 
Marked  pole,  88 

Mnrum  heating  by  discharge,  317 
Mascart,  E.,  on   atmospheric  elec- 
tricity, 335 

Matteucci,  Carlo,  on  physiological 
effects,  76,  256 

on     electromotive  -  force     in 

muscle,  257 
Maynooth     Battery    (sec     Callan's 

Battery) 

Maxwell,  James  Clerk,  Electro- 
magnetic theory  of  light, 
397,  518 

Law  of  alternate  currents,  473 


Maxwell,  James  Clerk,  Law  of 
electromagnetic  system,  204, 
349,  379 

measurement  of  "  v,"  859 
on  Electric  Images,  275 
on  protection  from  lightning, 

35,  332 

on  residual  charge  of  jar,  299 
rule  for  action  of  current  on 

magnet,  204,  349 
Theorem  of  equivalent  Mag- 
netic shell,  203,  351 
Theory  of  Magnetism,  126 

Measurement  of  capacity,  418 
of  currents,  221,  395,  412 
of  E.M.F.,  416 
of  internal  resistance,  417 
of  magnetic  forces,  130 
of  mutual  induction,  454 
of  permeability,  366 
of  power,  437 
of  resistance,  411,  412 
of  self-induction,  458 

Mechanical  depolarization,  180 

effects  of  discharge,  47,  315 
"      of  magnetization,  124 
"     in  dielectric,  299,  525 

Medical  Applications  of  Electricity, 
258 

Medium,  action  in,  5,  13,  279 

elasticity  and  density  of,  360 
enorgy  paths  in,  519 
velocity  of  waves,  in,  359,  518 

Mega-,  354 

Megohm,  354 

Meidinger's  Battery,  187 

Melloni,  Macedonia,  his  thermo- 
pile, 4-25 

Mendenfiall,  T.  C.,  U.  S.  Geodetic 
Survey,  155 

Meridian,  Magnetic,  151 

Metallo-chromy,  490 

Metals,   electro-chemical    power  of, 

489 

eloctro-deposition  of,  494 
refining  by  electricity,  494 
specific  resistance  of,  403 

Meter  Bridge,  415 

Meters,  442 

Metric  system,  the,  280 

Mho,  the,  402 

Mica,  dielectric  capacity  of,  296 

Micro-,  354 

Microfarad,  the,  283,  354 
condenser,  303 

Microphone,  the,  512 

Milli-,  354 


622 


ELECTRICITY   AND   MAGNETISM 


The  Numbers  refer  to  the  Numbered  Paragraphs. 

Milli-ampere,  354 

Mimosa,  tne  electric  behaviour  of,  256 

Minotto's  cell,  187 

Mirror  Galvanometer,  215 

Molecular  action  of  magnetism,  126 

actions  of  current,  249 

theory  of  Electric  action,  7 
Moment  of  Couple,  136 
Moment  of  circular  coil,  346 

of  inertia,  361 

magnetic,  135,  361 
Morse,  Samuel  F.  B.,  his  Telegraph 

instrument,  409 
Morse  Alphabets,  the,  499a 
Mordey's  alternator,  478 
Motion,  law  of,  in  magnetic  field, 

204,  379 

Motor-dynamos,  482 
Motors,  443 

alternate-current,  484 
Moulton,  John  Fletcher,  on  sensi- 
tive state,  322 

Mouse-mill  (see  Replenisher} 
Miiller,   Johannes,  on   strength  of 

electromagnets,  380 
Multicellular  voltmeter,  290 
Multiplier,  Schweigger's,  200 
Muscular  contractions,  255,  257 
Musschenbroek,    Peter    van,    dis- 
covery of  Leyden  jar,  00 

on  Magnetic  Figures,  121 
Mutual  induction,  454 

potential,  851 

NAPOLEON  III.  's  cell,  193 
Navigation,  electric,  443 
Needle,  magnetic,  87 
telegraph,  498 

Negative  electrification,  5,  327 
Network  mains,  440 
Neutralizing  brush,  50 
Newton,   Sir   Isaac,    observations 

on  action  and  reaction,  91 
his  lodestone,  114 
suggests     electric     origin     of 

lightning,  11,  329 
suggests     glass     for    electric 

machines,  41 
Niagara  Falls,  transmission  of  power 

from,  447 

Niaudet,  Alfred,  his  cell,  184 
Nickel,  93,  364 

Nobili,  Leopoldo,  on  muscular  con- 
tractions, 70 

on  currents    of  animal    elec- 
tricity, 257 
discovers  Nobili's  rings,  490 


Non-conductors,  10,  405 

Non-electrics,  3 

North  and  south,  89,  150 

magnetic  pole,  the,  89,  150 
Null  methods.  210,  289,  411  (c),  413, 
416  (6),  417  (e),  418  (d) 

OIU.IQUE  currents,  laws  of,  390 
Oersted,  Hans  Christian,  discovers 

magnetic  action  of  current, 

1<J5,  190,  202 

Ohm,  Dr.  Georg  Simon,  190 
"Ohm's  Law,"  191,  399 
Ohm,  the,  354,  and  Appendix  B 

evaluation  of,  358 
Oil,  dielectric  strength  of,  315 
One-fluid  theory  of  electricity,  7 
Opposition  method,  417 
Optical  strain,  electrostatic,  525 

rotation,  electromagnetic,  526, 

527,  528 
Oscillations,  electric,  332,  515 

method  of  (in  galvanometry), 

210 
method  of  (for  electrostatics), 

133  (footnote) 

method  of  (for  magnetic  mea- 
surement), 133,  134,  301 
Oscillator,  520,  522 
Osmose,  electric,  250 
Other  sources  of  electrification  than 

friction,  12,  65 
Output  of  dynamo,  464 
Over-compounding,  467 
Overhead  line  for  tram  cars,  446 
Oxvgen,  magnetic,  370 
Ozone,  237,  316,  329  (footnote) 

PA  ClNOTTrs  armature,  463 
Page,  Charles  G.,  discovers  mag- 
netic sounds,  124 
Parallel,  capacities  in,  307 

cells  in,  168,  406 

circuits,  laws  of,  390 

lamps  in,  453 

resistances  in,  409 

running  of  alternators,  479 
Paramagnetic  bodies,  369 
"  Passive  ".state  of  iron,  183 
Pathological  dose  of  current,  258 
Peace,  on  length  of  spark,  313 
Ptclet,  elcctriliciitioM  by  rubbing,  73 
Peltier,  Athanase,  his  electrometer, 
286,  334 

heating  effect  at  junctions,  420 

theory  of  thunderstorms,  330 


INDEX 


623 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Peltier  effect,  420 

Penetrative  power  of  discharge,  315 
Periodic  current,  470 
Periodicity     (see     Frequency}     of 
aurora  and  magnetic  storms, 
158,  159,  336 
Permeability,  96,  363,  518 

measurement  of,  366 
Perry,  John,  his  meter,  442 
Persistence  (see  Time-constant) 
Phase,  470,  472 

Phosphorescence     caused     by    dis- 
charge, 320,  321 
Photo-chemical  excitation,  530 
Photographic  plate  affected  by  dis- 
charge, 324 
Photophone,  529 
Photo-voltaic  property  of  selenium, 

529 

Physiological  actions,  254,  325 
Piercing  glass,  prevention  of,  62 
Piezo-elcctricitv,  75 
Plane,  the  proof-,  32 

for  magnetism,  232 
Plante,  Gaston,  secondary  cells,  492 

globular  lightning,  331 
Plants,  electricity  of,  77,  256 
Plate  condenser,' 56,  295,  304 

electrical  machine,  43 
Platinoid,  404 
Plucker,  Julius,  on  diamagnetism, 

etc.,  370,  373 
Poggendorff,  J.  C.,  his  cell,  180 

method  of  measuring  E.M.F., 

416 
Points,  density  of  charge  on,  38,  274 

discharge  at,  42.  45, 46,  47,  274, 

829 
Poisson,     magne-crystallic    action, 

373 
Polarity,  diamagnetic,  369 

magnetic,  90,  116,  126 
Polarization  (electrolytic)  in  battery 
cells,  175,  487 

of  Voltameter,  487,  492 

remedies  for,  180 

rotation  of  plane  of,  526  et  seq. 
Polarized  mechanism,  387 

relay,  501 
Poles  of  magnets,  86,  134 

of  pyroelectric  crystals,  74 

of  voltaic  battery,  168 
Polyphase  currents,  485 
Porous  cell,  ISO 
Porret's  phenomenon,  250 
Portable  electrometer,  287 
Portative  force,  114 


Post-Office  Bridge,  415 

relay,  501 
Positive  and  negative  electrification, 

5,  327 
Potential,  electric,  40,  263 

"        zero,  40,  264 
of  conducting  sphere,  269 
galvanometers,  220 
magnetic,  337,  347,  348 

"         due  to  current,  351 
mutual,  of  two  circuits,   352, 

357 

Potential-divider  mil  method,  418 
Potentiometer,  410 
Pouillet,  Claude  S.  M.,  sine  galvan- 
ometer, 214 

tangent  galvanometer,  212 
Powdered    metals,    conduction    of, 

400 

sensitiveness  to  sparks,  521 
Powders,  electroscopic,  31,  47,  299, 

324 
Power,  435 

transmission  of,  447 
Power-houses,  4-10 
Poynting,  John  Henry,  on  energy- 
paths,  519 
Practical  units,  354 
Preece,  William  Henry,  telegraphy, 

497 

Pressure  produces  electrification,  75 
effect  OH  electrolysis,  490 
(voltage),  169 

Priestley,   Joseph,   on  electric   ex- 
pansion, 300 

on  influence,  26  (footnote) 
Prime  conductor,  42 
Printing  telegraphs,  497 
Proof-plane,  32 

magnetic,  232 

Protoplasm,  electric  property  of,  256 
Pyroelectricity,  74 
Pyrometer,  404 

QUADRANT  electrometer  (Lord  Kel- 
vin's), 288 

electroscope  (Henley's),  17 
Quadruplex  telegraphy,  503 
"Quantity"  arrangement  of  cells, 

etc.,  192,  407 
of  electricity,  unit  of,  21,  262, 

354 

Quartz  fibre,  299 
Quartz,  no  residual  charge  from,  299 

as  insulator,  30,  299 
Quetelet,  E.,  on  atmospheric  elec- 
tricity, 333,  335 


624 


ELECTRICITY   AND   MAGNETISM 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Quincke,     Georg,     on    diaphragm 

currents,  252 
on  electric  expansion,  300 
on    electro-optic    phenomena, 

525 
Quinine,  use  of,  for  mapping  fields, 


RADIANT  state  of  matter,  321 

Kadio-micrometer,  425 

Kate  of  change  of  current,  454,  472 

(footnote) 

Ratio    of    electrostatic    to    electro- 
magnet units,  283,  359 
Ray,  electric  (torpedo),  76 
Rays,  kathodic,  321 

current  balance,  396 
Rayleigh,    Lord,  determination   of 

ohm,  358 
Reactance,  473 
Reciprocal  accumulation,  49 
Recording  instruments,  160,  334 
Redistribution  of  charge,  39 
Reduction  of  metals,  494 
Reflecting  galvanometer,  215 
Reflexion  of  electric  waves,  520 
Refractive  index,  518 
Registering  magnetographs  and  elec- 
trometers, 160,  334 
Reis,  Philipp,    invention    of   tele- 
phone, 510 
Relays,  501 
Reluctance,  375 
Reluctivity,  375  (footnote) 
Remanence,  367 
Replenisher,  49,  287,  288 
Repulsion  and  attraction  of  electri- 
fied bodies,  2, 4, 22, 24, 74, 262 
and    attraction,    experiments 

on,  47 
and    attraction    of     currents, 

338,  389,  394 
and  attraction  of  magnets,  84, 

88 

Repulsion  electrometers,  286 
Residual  charge  of  Leyden  jar,  61, 

299 
Residual  charge  of  cable,  301 

of  Voltameter,  492 
magnetism,  112,  127,  367 
Resinous  electricity,  5 
Resistance  and  heat,  426 
Resistance,  30,  171,  400,  426 

affected  by  temperature,  404 
light,  529 
magnetism,  397 
sound,  512 


Resistance,  as  a  velocity,  357 

bridge  or  balance,  413 

coils,  414 

internal,  of  cell,  192,  407,  417 

internal,  of  cell,  measurement 
of,  417 

laws  of,  400 

magnetic,  375 

measurement  of,  411  et  sea. 

of  gases,  171,322 

of  glow  lamps,  452 

of  human  body,  255 

of  liquids,  171,  403 

of  vacuum,  321 

specific,  403 

to  alternate  currents,  476 

units  of,  352  et  seq. 
Resistivity,  402 
Resonance,  517 
Resonator,  520 

Resultant  magnetic  force,  115 
Retardation     of    currents    through 

cables,  301,  323,  505 
Retentivity  (magnetic),  98,  367 
Return  shock  or  stroke,  29,  331 
Reversal  of  influence  machines,  53 
Reversibility  of  processes  in  circuit, 

248,  436 

Reversing-switch,  230,  498 
Reymond,    Du    Bois,    his    galvan- 
ometer, 257 

on  animal  electricity,  257 

unpolarizable  electrodes,  257 
Rheostats,  400 
Rheometer,   "} 

Rheoscope,     !>  see  footnote  to  208 
Rheotrope,    J 

Riess,  Peter,  on  electric  distribution, 
38 

on  length  of  spark,  313 

electric  thermometer,  317 
Ritchie,  magnetic  circuit,  375 

his  motor,  443 

Ritter,  Johann   Wilhelm,  on  action 
of  current  on  sight,  254 

his  secondary  pile,  492 

on  subjective  galvanic  sounds, 
254 

on  the  sensitive  plant,  256 
Rolling  friction,  12,  73 
Romagnosi,  Dr.,  discovers  magnetic 

action  of  current,  195 
Romas,  De,  his  electric  kite,  329 
Ronalds,  Sir  Francis,  invented  a 

telegraph,  497 

Rotation  of  plane    of  polarization, 
526 


INDEX 


625 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Rotations,  electromagnetic,  393 

Arago's,  457 

Rotatory  magnetic  field,  485 
Roughness  of  surface  as  depolarizer, 

180 

Rowland,  Henry  A.,  on  magnetic 
effect  of  electric  convexion, 
397 

on  magnetic  circuit,  375 
Riicker,  Arthur  William,  on  ration- 
alization of  dimensions,  300 
Kiicker  and  Thorpe,  magnetic  sur- 
vey, 154 

Ruhmkorff's  electromagnet,  369 
induction  coil,  '229 
coil,  mutual  induction  of,  454 

ST.  ELMO'S  FIRE,  329  (footnote) 
Safety-fuses,  429 
Salts,  electrolysis  of,  23S,  490 
Sanderson,  J.  Burdon,  on  electric 

sensitiveness  of  carnivorous 

plants,  256 

Saturation,  magnetic,  112,  363  et  seq. 
Savery,  85 
Sawdust  battery,  1S7 
Schallenberger's  meter,  442 
Schuclcert,  ammeter,  221 
Schuster,  Arthur,  on  electrolysis  of 

gases,  322 

Schweigger's  multiplier,  200 
Screening,  magnetic,  96 
inductive,  514 
of  eddy-currents,  457,  514 
Secohm,  453 
Secondary    actions    in    electrolysis, 

Secondary  batteries,  492 
Secular  variations  of  magnetic  ele- 
ments, 155 
Seebeck,   Thomas    Johann,   effect, 

419 

Selenium,  photo-electric  properties 
of,  529 

resistance  of,  403  (table),  529 
Self-exciting  influence  machine,  50 

dvnamo,  462 
Self-induction,  458,  472 

in  electric  discharge,  515 
Self-recording  instruments,  160,  334 
Semaphore,  Henley's,  17 
Sensitive  plant,  behaviour  of,  256 
Series,  arc  lamps  in,  450 

capacities  in,  308 

cells  in,  168,  406 

dynamos,  465 

resistances  in,  406 

28 


Serrin,  Victor,  his  lamp,  449 

Shadows,  electric,  47 

in  partial  vacuum,  321 

Sheet  conductor,  flow  of  electricity 
in,  410 

Shell,  magnetic,  118,  203,  350 
potential  due  to,  348 

Shielding,  magnetic,  97 

Shock,  electric,  254,  325 

Shunt,  215,  409 

coil  in  arc  lamps,  449 
dynamo,  465 

Shuttle  armature,  461 

Siemens,  Alexander,  on  length  of 
spark,  313 

Siemens,     Werner,    on    dynamos, 

461 

mercury  unit,  358 
electrodynamometer,  395 
shuttle-wound  armature,  461 
heating  in  Leyden  jar,  299 

Sight  affected  by  current,  254 

Silurus,  the,  76 

Sine  galvanometer,  214 

Sine  law,  476 

Single-fluid  cells,  180 

Single-needle  instrument,  498 

Single  touch,  100 

Siphon  recorder,  506 

Skew-symmetry  of  crystals,  75 

Skin  effect,  476 

Skin,  E.M.F.  in  the,  257 

Smee,  Alfred,  his  Battery,  180 

Smith,  Frederick  John,  effect  on 


Smith 


photographic  plate,  :>'24 
,    Willoughby,   on   selenium, 


5211 


Soap-bubble,  electrified,  4 
Sodium  by  electrolysis,  490 
Solenoid  arc  lamps,  449 
Solenoid,  385 

magnetizing  force  of,  341 
Solid  angles,  148  (Appendix  A) 
Solidification,  69 

Sound  of  magnetization,  124,  510 
Sounder,  the,  497 
Sources  of  electricity,  12,  65 
Spark,  11,  46,  47,  310 

duration  of,  323 

length  of,  48,  313,  329 
Sparking  at  commutator,  463 
Specific  resistance,  4u:} 

inductive  capacity,  25,  56,  295, 

299 
Speed  of  motor,  444 

of  signalling,  301,  302,  323 


ELECTRICITY  AND   MAGNETISM 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Sphere,  distribution  of  charge  over, 
38,  273  et  seq. 

potential  of,  209,  271 

capacity  of,  271 
Spiral  shortens  itself,  390 
Spottiswoode.    William,   on   stria?, 

322 

Square  root  of  mean  square,  471 
Standard  cells,  188 

effect  of  temperature  on,  194 
Standards,  354 
Steel  hardening,  108 
Steel,  properties  of,  362 

facing,  495 

Stewart,  Balfour,  on  atmospheric 
electricity,  335 

on  magnetic  storms,  158 
Storms,  magnetic,  159 
Straight  conductor  force  near,  207, 

343 

Strain,  dielectric,  64,  299,  525 
Strength  of  current,  1T1,  190,  354 

of  current  in  magnetic  mea- 
sure, 206,  207,  353  et  seq. 

of  dielectric,  299,  311 

of  magnet  pole,  112,  352 

of  magnetic  shell,  348 
Stress,  electric,  13,  16,  20,  22,  24,  63, 
279,  299,  311,  525 

electric,  optical  effect  of,  525 

magnetic,  119,  340,  389 
Striae  in  vacuum  tubes,  320,  322 
Sturgeon,    William,  his  commuta- 
tor, 461 

electro-magnets,  381 

on  magnetic  circuit,  375 

induction  coil,  229 
Submarine  telegraphs,  504 
Sucking-magnet,  385 
Sulphur  as  depolarizer,  185 
Sulphuretted  hydrogen,  iron   nega- 
tive to  copper  in,  80 
Sulzer's  experiment,  254 
Supply  meters,  442 
Surface  contact,  12 

density  of  charge,  38,  273 

limit  of,  273 

of  magnetism,  134,  337 
Surgical  applications,  258 
Susceptibility,  365 
Suspended-coil  galvanometers,  216 
Swammerdam  s    frog    experiment, 

255 

Swan's  incandescent  lamp,  452i 
Symmer,  on  two  kinds  of  electrilica- 

tion,  5 
Synchronizing,  479 


TAIT,  PETER  GUTHRIE,  electrifica- 
tion by  evaporation  of  sul- 
phate of  copper  solution,  71 
heating  of  iron  electrode,  433 
thermo-electric  diagram,  424 
Tangent  galvanometer,  212 

of  angle  of  lag,  473 
Tapper,  498 

Taste  affected  by  current,  254 
Telegraph,  electric,  497 

Bain's  chemical,  246 
Morse's  instrument,  499 
needle  instrument,  498 
Telegraphy,  diplex,  503 
duplex,  503 
quadruplex,  503 
submarine,  504 

Telephone,  Philipp  fieis's,  510 
currents  of,  255 
Dolbear's,  299,  511 
Edison's  (carbon),  511 
Graham  BelVs  (articulating), 

510 

Farley's  (condenser),  299,  511 
Exchanges,  513 
Temperature  affects  resistance,  194, 

404 

affected  by  resistance,  426 
effect  on  length  of  spark,  313, 

314 

of  the  arc,  448 
Tempering  of  steel,  108 
Tension,  electric,  13,  16,  20,  22,  24, 
63,  273  (footnote),  279,  299, 
311,  525 

Terquem,  A.,    parrot-cage    experi- 
ment, 34 
Terrestrial  Magnetism,  95,  150,  361, 

365 
Test  for  weak  currents  (chemical), 

246,  316 

for  weak  currents  (physiologi- 
cal), 255 

Testing  for  faults,  502 
Tetanization     produced     by    inter- 
rupted currents,  256 
Theories  of  Electricity,  7,  327,  and 

Preface,  ix 
Theories  of  Magnetism,  99,  126 

Ampere's,  398 
"      Ewing's,  127 
"      Maxwell's,  126 
"       Weber's,  126,  127 
Theory  of  Electrolysis,  Grotthuss's 

and  Clausms's,  4!)1 
Theory  of  Earth's  magnetism,  161 
of  Light,  518 


INDEX 


627 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Thermo-electric  currents,  |  - 

Thermo-electricity,  )  ' 

Thermo-electric  Diagram,  424 

Thermo-electromotive  Series,  424 

Tliermopile,  425 

Thompson,  Silvanus   Phillips,  on 
magnetic  figures  due  to  cur- 
rents, 202,  3S9 
on     positive      and      negative 

states,  327 
on  opacity  of  tourmaline,  518 

Thomson,  Joseph   J.,   on   Contact 

Electricity,  81 

on     conductivity      of     gases, 
322 

Thomson,  Sir  William  (see  Kelvin, 

Lord) 
effect,  424 

Thomson,  Elihu,  his  meter,  442 

on  alternate-current  magnets, 

477 
on  welding,  433 

Thomson-Houston   dynamos,    468, 
478 

Thorpe  and  Riicker,  magnetic  sur- 
vey, 154 

Three  wire  system,  453 

Thunder,  11,  331 

Thunderstorms,  329 
Theory  of,  330 

Time-constant,  460 

Tinfoil  Condensers,  55,  302 

Tivoli,  transmission  of  power  from, 
447 

Toepler,  A.,  his  Influence  Machine, 
51 

Tongs,  Discharging,  59 

Torpedo  (electric  fish),  76,  246 

Torpedoes,    fuzes    for    firing,    316, 

Torque,  136 

Torque  of  motor,  444 

Torsion   affected  by   magnetization, 

124 

Torsion  Balance,  or       )   Coulomb's, 
Torsion  Electrometer,  f       18,  132 
Torsion  method,  209,  210 
Tourmaline,  74,  324,  518 
Transformers,  228,  480 

for  vacuum  tubes,  320 
Transmission  of  power,  447,  479 
Tri-phase,  485 

Trolley  wheel  for  tramcars,  446 
Trowbridge,  on    magnetization    at 

-100°C.,  Ill 
Tube  of  force,  337  (g) 
Tuning-fork  method,  418 


Two-fluid  cells,  181 

theory,  7 

Two  kinds  of  Electrification,  5,  6 
"        Magnetic  poles,  89 
Tyndall,  John,  diamagnetic  polarity, 

372 
magne-crystallic  action,  373 


ULTRA-GASEOUS  MATTER,  821 
Ultra-violet  waves,  313 

discharge  by,  531 

effect  on  metal,  531 
Unit,  Board  of  Trade,  440,  488 
Unit  jar,  285 

Units  and  standards,  Board  of  Trade 
(see  Appendix  B) 

electromagnetic,  352  et  seq. 

electrostatic,  283  et  seq. 

fundamental  and  derived,  281, 
282 

ratio  of  electrostatic  to  electro- 
magnetic, 262  (footnote), 
283,  359 

Unipolar  Machines,  469 
Universal  Discharger,  62 
Unvarying  magnets,  110 
Upward,  his  cell,  193 
Ure,  Dr.,  on  animal  electricity,  255 


"v,"359,  518 

Vacuum,     induction      takes     place 

through,  64,  96,  97 
partial,  spark  in,  11,  320 
spark  will  not  pass  through, 

313,  321 
tubes,  320,  321 

"  Variation,"  the  (see  Declination) 
Variation  of  Declination  and  Dip  — 
annual,  157 
diurnal,  156 
geographical,  151,  154 
secular,  155 

of  electrification  of  the  atmos- 
phere, 335 
Varley,   Cromwell  Fleetwood,  his 

galvanometer,  316 
on    capacity    of   polarization, 

492 

telegraph,  497 

Varley,  Samuel   Alfred,  his  tele- 
phone, 299,  510 
early  dynamo,  462 
Vegetables,  Electricity  of,  77 

carnivorous,  sensitiveness  of, 
256 


628 


ELECTRICITY   AND   MAGNETISM 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Velocity  of  discharge,  323 

of  light,  359,  518 

of  electric  waves,  518 

of  rubbing,  electrification  de- 
pends on,  73 

resistance  as  a,  357 
Verdet's  constant,  526 
Vibration     produces  Electrification, 

67 

Vibrator  for  measuring  capacity,  418 
Villari,  JSmilio,  effect  of  tension, 

364 

Violet  waves  (see  Ultra-violet) 
Virtual  volts  and  amperes,  471 
Vitreous  electricity,  5 
Volt,  109,  354 

Volt  a,     Alessandro,    his    Electro- 
phorus,  26 

Condensing  Electroscope,  79 

Contact  Series,  80 

Crown  of  Cups,  165 

on    Atmospheric    Electricity, 
334 

on  Contact  Electricity,  79,  163 

on  Electric  Expansion,  300 

on  Electrification  due  to  com- 
bustion, 70 

Subjective  Sounds  due  to  Cur- 
rent, 254 

Voltrfs  Law,  80,  163,  170 

Voltaic  Pile,  164 

Voltaic     Electricity    (see     Current 
Electricity} 

arc,  448 

battery,  168,  178 ;  pile,  164 

cell,  simple,  166 
Voltameter,  242,  243,  244,  487 
Voltmeter,  220 

Cardew's,  430 

electrostatic,  290 
Voss  machine,  51 


WALKER,  CHARLES  F.,  used  sulphur 

in  cell,  1S5 

Warburg,  E.,  on  hysteresis,  368 
Water,  Electrolysis  of,  235,  487 
Water-dropping,  discharge  by,  334 
Watt,  the,  354,  435 
Wattmeter,  438 
Watts,  true  and  apparent,  475 


Waves,  electric,  515 

Weber,  the,  354 

Weber,  Wilhelm,  the  Electro-dyna- 

mometer, 394 

on  diamagnetic  polarity,  372 
evaluation  of  ohm,  358 
of  "v,"  359 

theory  of  magnetism,  126,  127 
Wrelding,  433 

Weston,  Edward,  voltmeter,  220 
standard  cell,  188 
temperature      coefficient      of 

alloys,  404 
Wheatstone,   Sir   Charles,  on  the 

brush  discharge,  319 
Automatic  Telegraph,  497 
Dynamo  -  electric      Machines, 

462 
on  supposed  velocity  of  elec- 

tricity, 323 
Wheafstone's  Bridge  or  Bal- 

ance, 413 

Whirls,  magnetic,  202,  389 
Wiedemann,    Gustav,  on  effect  of 

magnetism  on  torsion,  124 
diamagnetism,  370  (footnote) 
Wilde,     Henry,     Magneto  -  electric 

Machine,  462 
WilcJce,  A.,  electrophorus,  26  (foot- 

note") 
Wimshurst,   James,  Influence  ma- 

chine, 52 

Wind,  electric,  47,  324 
Winding  of  electromagnets,   375  et 
seq.,   385,    386  (and   see   p. 
696) 

Window,  aluminum,  321 
Wohlers  cell,  193 
Wollastoris  Battery,  180 
Work    by   conductor  cutting    lines, 

339 

Wrobleivski,  resistance  of,  at   low 
temperatures,  404 


Pile,  16,  193,  291 
Zanotti,     experiment      on      grass- 

hopper, 255 
Zero  potential,  40,  264 
Zero  of  temperature,  resistance  near, 

404 
Zinc  as  fuel,  166 


THE     END 


MACMILLAN    &    CO.'S 

PUBLICATIONS     ON 

ELECTRICITY  ^  MAGNETISM 


BOTTONE.  —A  Guide  to  Electric  Lighting.  By  R.  S.  BOTTONE, 
author  of  "  Electric  Bells,  and  All  About  Them,"  "  Electro- 
motors, How  Made  and  How  Used,"  etc.  With  many  Illus- 
trations. 75  cents. 

CAVENDISH.  — The  Electrical  Researches  of  the  Honourable 
Henry  Cavendish,  F.R.S.  Written  between  1771  and  1781. 
Edited  from  the  original  manuscripts  by  the  late  J.  CLERK 
MAXWELL,  F.R.S.  8vo.  $5.00. 

GUMMING.— An  Introduction  to  the  Theory  of  Electricity.  By 
LINNAEUS  GUMMING,  M.A.  With  Illustrations.  i2mo.  $2.25. 

DAY.— Electric  Light  Arithmetic.  By  R.  E.  DAY,  M.A.  i8mo. 
40  cents. 

"  I  have  not  thought  it  necessary  to  go  into  minute  details  about  electrical 
formulae  and  theories,  because  these  will  be  found  in  all  the  recognized  text- 
books on  the  subject,  and  this  collection  of  examples  is  not  intended  to  re- 
place, but  to  supplement,  whatever  text-book  on  electricity  the  student  may 
be  using."  —  From  the  Author  s  Preface. 

EMTAGE.  — An  Introduction  to  the  Mathematical  Theory  of 
Electricity  and  Magnetism.  By  W.  T.  A.  EMTAGE,  M.A.,  of 
Pembroke  College,  Oxford.  121110.  $1.90. 

"  This  book  has  been  written  with  the  object  of  supplying  an  Introduc- 
tion to  the  Mathematical  Treatment  of  Electricity  and  Magnetism.  ...  It 
is  complete  in  itself,  and  may  be  read  without  previous  knowledge  of  the 
subject.  Purely  experimental  parts  of  the  subject,  requiring  no  special 
mathematical  treatment,  have  been  entirely  omitted."  —  From  the  A  uthor's 
Preface. 

"  The  book  is  chiefly  valuable  for  the  care  and  accuracy  with  which  the 
fundamental  ideas  of  the  subject  are  defined,  and  the  elementary  laws  stated. 
It  gives  the  latest  developments  of  the  more  elementary  parts  of  the  mathe- 
matical theory  of  electricity,  and  will  prove  useful  for  the  student  preparing 
for  examination."  —  Scotsman. 

GRAY.  —  The  Theory  and  Practice  of  Absolute  Measurements  in 
Electricity  and  Magnetism.  By  ANDREW  GRAY,  M.A., 
F.R.S.E.  In  two  volumes.  Vol.  I.,  i2mo.  $3.25. 


MACMILLAN    &    CO.,  PUBLISHERS, 

68  FIFTH  AVENUE,        -  NEW  YOKK. 


WORKS   ON  ELECTRICITY  AND  MAGNETISM. 


GRAY.  —  Absolute  Measurements  in  Electricity  and  Magnetism 
for  Beginners.  By  ANDREW  GRAY,  M.A.,  F.R.S.E.  Students' 
edition  abridged  from  the  larger  work.  i6mo.  $1.25. 

GUILLEMIN.  —  Electricity  and  Magnetism.  A  Popular  Treatise. 
By  AM£DEE  GUILLEMIN,  author  of  "  The  Forces  of  Nature," 
"  The  Applications  of  Physical  Forces,"  etc.  Translated  and 
Edited,  with  Additions  and  Notes,  by  Professor  Silvanus  P. 
Thompson,  author  of  "  Elementary  Lessons  in  Electricity  and 
Magnetism,"  etc.  With  600  Illustrations.  Super  Royal  8vo. 
$8.00. 

"  In  the  first  part  M.  Guillemin  expounds  with  his  usual  skill  the  phe- 
nomena and  laws  of  electricity  and  magnetism;  and  in  the  second  part  he 
considers  the  applications  in  modern  life  of  these  two  wonder-working  forces. 
...  It  will  undoubtedly  receive,  as  it  deserves,  the  same  warm  reception 
as  its  predecessors  from  the  same  hand." —  The  Literary  World. 

LODGE.  —  Modem  Views  of  Electricity.  By  OLIVER  J.  LODGE, 
LL.D.,  D.Sc.,  F.R.S.  With  Illustrations.  i2mo.  $2.00. 

"  This  book  is  likely  to  attract  much  attention  in  the  electrical  world. 
It  aims  at  setting  forth  in  popular  guise  the  results  of  modern  attempts  to 
explain  the  phenomena  of  electricity,  magnetism,  and  light,  by  known  prin- 
ciples of  mechanics  and  hydrodynamics.  .  .  .  Dr.  Lodge  is  an  admirable 
exponent.  ...  To  those  who  value  science  chiefly  for  its  practical  applica- 
tions, the  most  interesting  portion  of  the  book  will  be  that  which  proposes 
the  direct  manufacture  of  light."  —  London  Atheneenm. 

MAXWELL.  — An  Elementary  Treatise  on  Electricity.  By 
JAMES  CLERK  MAXWELL,  M.A.  Edited  by  WILLIAM  GAR- 
NETT,  M.A.  Second  edition.  Clarendon  Press  Series.  8vo. 
$1.90. 

MAXWELL.  — A  Treatise  on  Electricity  and  Magnetism.  By 
JAMES  CLERK  MAXWELL.  M.A.  Clarendon  Press  Series.  Two 
volumes.  8vo.  New  Edition.  $8.00, 

MAYCOCK.  —  A  First  Book  of  Electricity  and  Magnetism.     For 

the  Use  of  Elementary  Science  and  Art  and  Engineering  Stu- 
dents and  General  Readers.  By  W.  PERREN  MAYCOCK, 
M.I.E.E.  With  84  Illustrations.  Crown  8vo.  60  cents. 

MURDOCK.  —  Notes  on  Electricity  and  Magnetism.  Designed 
as  a  companion  to  Silvanus  P.  Thompson's  "  Elementary  Les- 
sons in  Electricity  and  Magnetism."  By  J.  B.  MURDOCK, 
Lieut.  U.  S.  N.  i8mo.  New  Edition.  60  cents. 

"  Occasional  extensions  and  additions  are  also  made  which  add  much 
value  to  the  book.  It  is  likely  to  be  of  considerable  use  to  the  student  of 
Professor  Thompson's  '  Elementary  Lessons,'  and  it  may  be  used  alone  with 
little  difficulty."  —  Science. 


MACMILLAN    &    CO.,  PUBLISHERS, 

66  FIFTH  AVENUE,        ....        NEW  YOBK. 


WORKS   ON  ELECTRICITY  AND  MAGNETISM. 


POOLE.  —  The  Practical  Telephone  Handbook.  By  JOSEPH 
POOLE.  With  227  Illustrations.  Small  crown  8vo.  $1.00. 

STEWART  and  GEE.— Practical  Physics  for  Schools  and  Junior 
Students  of  Colleges.  By  BALFOUR  STEWART,  M.A.,  LL.D., 
F.R.S.,  and  W.  W.  HALDANE  GEE,  B.Sc. 

Vol.  I.    ELECTRICITY  AND  MAGNETISM.    i6mo.    60  cents. 

"  The  authors  have  succeeded  in  presenting  the  subject  in  such  a  way 
that  it  may  be  easily  grasped  by  the  class  in  schools;  and  the  more  difficult 
parts  make  an  excellent  introduction  to  advanced  work.  .  .  .  We  can 
heartily  recommend  the  book  to  those  about  to  take  up  the  study  of  elec- 
tricity."— Electrical  World. 

STEWART  and  GEE.  —  Lessons  in  Elementary  Practical  Phys- 
ics. By  BALFOUR  STEWART,  M.A.,  LL.D.,  F.R.S.,  and  W.  W. 
HALDANE  GEE,  B.Sc. 

Vol.  II.    ELECTRICITY  AND  MAGNETISM,    izmo.    $2.25. 

"  Not  a  book  to  be  read  straight  through,  this  work  of  Messrs.  Stewart 
and  Gee  is  one  to  be  worked  steadily  through  by  any  student  who  intends  to 
acquire  a  real  knowledge  of  the  principles  of  electricity  and  magnetism."  — 
Journal  of  Education. 

"  The  book  is  essentially  an  exposition  of  those  parts  of  electrical  phil- 
osophy with  which  the  student  who  would  become  an  electrician  must  neces- 
sarily be  acquainted.  It  is  well  illustrated,  clearly  arranged,  and  well  printed, 
and  is  likely  to  be  of  valuable  aid  to  students."  — The  Westminster  Review. 

THOMSON.  —  Reprints  of  Papers  on  Electrostatics  and  Mag- 
netism. By  Sir  WILLIAM  THOMSON,  D.C.L.,  LL.D.,  F.R.S., 
F.R.S.E.  8vo.  .  #5.00. 

THOMPSON.  — Elementary  Lessons  in  Electricity  and  Magnet- 
ism. By  SILVANUS  P.  THOMPSON,  D.Sc.,  B.A.,  F.R.A.S.  New 
Edition.  With  Illustrations.  i6mo.  $1.40. 

"  The  best  book  for  its  expressed  purpose  that  I  happen  to  be  acquainted 
with."  — Prof.  A.  V.  DOI.BEAR,  Tufts  College. 

"  The  text-book  itself  is  a  model  of  what  an  elementary  work  should  be. 
.  .  .  We  do  not  think  that  any  student  of  moderate  intelligence  who  reads 
this  work  slowly  and  with  care,  could  fail  to  understand  every  word  of  it,  and 
yet  every  part  of  the  complex  and  manifold  phenomena  of  electricity  and 
magnetism  is  treated  of  in  this  small  volume."  —  Saturday  Review. 

WATSON  and  BURBURY.  —  The  Mathematical  Theory  of  Elec- 
tricity and  Magnetism.  By  H.  W.  WATSON,  D.Sc.,  F.R.S., 
and  S.  H.  BURBURY,  M.A. 

Vol.   I.    ELECTROSTATICS.    8vo.    $2.75. 

Vol.  II.    MAGNETISM  AND  ELECTRODYNAMICS.    8vo.    $2.60. 


MACMILLAN    &    CO.,  PUBLISHERS, 

66  FIFTH  AVENUE,        -  NEW  YOBK. 

3  . 


WORKS  ON  ELECTRICITY  AND  MAGNETISM. 


LIGHTNING    CONDUCTORS   and    LIGHTNING   GUARDS.    By 

Professor  OLIVER  J.  LODGE,  D.Sc.,  F.R.S.,  M.I.E.E.    With 
numerous  Illustrations,     ismo.    Cloth.     $4.00.     [/« the  Press. 

ELECTRIC  LIGHT  CABLES  AND  THE  DISTRIBUTION  OF 
ELECTRICITY.  By  STUART  A.  RUSSELL,  A.M.I.C.E.  With 
over  zoo  Illustrations.  I2mo.  $2.25. 

THE  DYNAMO.  By  C.  C.  HAWKINS,  A.M.I.C.E.,  and  J.  WAL- 
LACE. i2mo.  Cloth,  $3.00. 

THE  PRACTICAL  TELEPHONE  HANDBOOK.  By  JOSEPH 
POOLE.  With  227  Illustrations.  Small  crown  8vo.  $1.00. 

A  FIRST  BOOK  OF  ELECTRICITY  AND   MAGNETISM.     By 

W.  PERRIN  MAYCOCK,  M.I.E.E.,  author  of  "  Practical  Elec- 
trical   Notes    and    Definitions."     With    Illustrations.     Small 
crown  8vo.     60  cents. 
INDUCTION  COILS.     By  G.  E.  BONNEY.     i2mo.     Cloth.    $1.00. 

COLLIERY  LIGHTING  BY  ELECTRICITY.  By  SYDNEY  F. 
WALKER,  M.I.E.E.,  author  of  "  Electricity  in  Our  Homes  and 
Workshops."  i2mo.  Cloth  lined.  75  cents. 

TOWN  LIGHTING  BY  ELECTRICITY.  By  SIDNEY  F.  WALKER, 
M.I.E.E.,  authoV  of  "  Electricity  in  Our  Homes  and  Work- 
shops." Illustrated.  \In  the  Press. 

A  GUIDE  TO  ELECTRIC  LIGHTING.  For  Householders  and 
Amateurs.  By  S.  R.  BOTTONE,  author  of  "  Electrical  Instru- 
ment Making,"  "  Electromotors,"  "  Electric  Bells,"  etc.  With 
many  Illustrations.  75  cents. 

A  popular  guide  by  a  well-known  writer,  giving  in  clear  and  easily  un- 
derstood language  the  information  necessary  to  those  about  to  introduce  the 
Electric  Light  into  their  dwellings. 


MACMILLAN  &  CO.,  PUBLISHERS, 

66  FIFTH  AVENUE,        -        ...        NEW  YORK. 


[URN     ENGINEERING  LIBRARY 

>— *>  642-3366 


^N  PERIOD  1 

2 

3 

5 

6 

ALL  BOOKS  MAY  BE  RECALLED  AFTER  7  DAYS 
Dverdues  subject  to  replacement  charges 


DUE  AS  STAMPED  BELOW 

^^^^A/^^_ 
FM^VM^^I 

>tNT  ON  ILL 

UN  t  6  199/| 

C.  BERKELEY 

UNIVERSITY  OF  CALIFORNIA,  BERKELEY 
NO.  DD1 1 ,  80m,  8/80  BERKELEY,  CA  94720 


VB  23989 


749219 


Engineering' 
Libraiy 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


